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=J:B:::::::::::::::::::jysy:>:<:::::::::::::::::::vYxI:;Z::::::::::1:
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT 302 4 "a) \+
 " }{XPPEDIT 303 1 "1;" "6#\"\"\"" }{TEXT 304 9 "     b)  " }{XPPEDIT 
305 1 "2;" "6#\"\"#" }{TEXT 306 10 "      c)  " }{XPPEDIT 307 1 "3;" "
6#\"\"$" }{TEXT 308 7 "    d) " }{XPPEDIT 309 1 "4;" "6#\"\"%" }{TEXT 
310 10 "      e)  " }{XPPEDIT 311 1 "5;" "6#\"\"&" }{TEXT 312 11 "    \+
    f) " }{XPPEDIT 313 1 "6;" "6#\"\"'" }{TEXT 314 11 "       g)  " }
{XPPEDIT 315 1 "7;" "6#\"\"(" }{TEXT 316 8 "    h)  " }{XPPEDIT 317 1 
"8;" "6#\"\")" }{TEXT 318 8 "     i) " }{XPPEDIT 319 1 "9;" "6#\"\"*" 
}{TEXT 320 80 "                          \nj) Insufficient information
 to determine the answer  " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 496 
16 "Answer:    ( d )" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 36 "F := vector([-7,8]) + vector([a,b]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"FG,&-%'vectorG6#7$!\"(\"\")\"\"\"-F'6#7$%\"aG%\"bGF
," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "F := evalm(F);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG-%'vectorG6#7$,&\"\"(!\"\"%\"aG
\"\"\",&\"\")F-%\"bGF-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "e
qn1 := vectorLength(F) = sqrt(145);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%%eqn1G/*$,,\"$8\"\"\"\"*&\"#9F)%\"aGF)!\"\"*$)F,\"\"#F)F)*&\"#;F)%
\"bGF)F)*$)F3F0F)F)#F)F0*$\"$X\"F6" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "eqn2 := F[2] = 12*F[1];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%%eqn2G/,&\"\")\"\"\"%\"bGF(,&\"#%)!\"\"*&\"#7F(%\"aGF(F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "solve( \{eqn1,eqn2\} , \{a,b
\} );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<$/%\"aG\"\")/%\"bG\"\"%<$/F%
\"\"'/F(!#?" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" 
{TEXT 260 18 "3. Suppose that   " }{TEXT 546 1 "v" }{TEXT 547 8 "  and
   " }{TEXT 548 1 "w" }{TEXT 549 21 "  are vectors with   " }{TEXT 
542 1 "v" }{TEXT 543 1 " " }{TEXT 540 1 "x" }{TEXT 541 1 " " }{TEXT 
544 1 "w" }{TEXT 545 2 "  " }{TEXT 550 1 "=" }{TEXT 551 1 " " }{TEXT 
328 1 " " }{XPPEDIT 488 0 "`<`;" "6#%\"<G" }{TEXT 484 1 " " }{XPPEDIT 
492 1 "-1,-5,4;" "6%,$\"\"\"!\"\",$\"\"&F%\"\"%" }{TEXT 325 1 " " }
{XPPEDIT 489 0 "`>`;" "6#%\">G" }{TEXT 487 3 " . " }{TEXT 493 7 " \nIf
   " }{TEXT 552 6 "v  =  " }{XPPEDIT 490 0 "`<`;" "6#%\"<G" }{TEXT 
485 1 " " }{XPPEDIT 329 1 "3,1,c;" "6%\"\"$\"\"\"%\"cG" }{TEXT 326 2 "
  " }{XPPEDIT 491 0 "`>`;" "6#%\">G" }{TEXT 486 17 " ,   then what is
" }{TEXT 330 2 "  " }{XPPEDIT 331 1 "c;" "6#%\"cG" }{TEXT 327 1 " " }
{TEXT 332 2 "? " }{TEXT 333 2 "  " }}{PARA 3 "" 0 "" {TEXT 274 211 "\n
a) -4              b) -3            c)  -2           d) -1            \+
  e)  0         \n f)   1             g)  2            h) 3           \+
   i)  4               j)  insufficient information to answer question
 " }{TEXT 334 7 "      \n" }}{PARA 0 "" 0 "" {TEXT 497 16 "Answer:    \+
( g )" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 10 "Whatever  " }{TEXT 553 1 "w" }{TEXT -1 7 "  is,  " }
{TEXT 554 1 "v" }{TEXT -1 24 "  is perpendicular to   " }{TEXT 556 2 "
v " }{TEXT 555 1 "x" }{TEXT 557 2 " w" }{TEXT -1 1 "." }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "eqn := do
tprod( [3,1,c],[-1,-5,4]) = 0 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$
eqnG/,&\"\")!\"\"*&\"\"%\"\"\"%\"cGF+F+\"\"!" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 18 "c = solve(eqn, c);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/%\"cG\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 261 1 " " }{TEXT 341 
36 "4. What is the angle between vectors" }{TEXT 342 3 "   " }
{XPPEDIT 339 1 "`<`*2,3,1*`>`;" "6%*&%\"<G\"\"\"\"\"#F%\"\"$*&F%F%%\">
GF%" }{TEXT 335 1 " " }{TEXT 337 3 "and" }{TEXT 338 2 "  " }{XPPEDIT 
340 1 "`<`*3,1,(-2)*`>`;" "6%*&%\"<G\"\"\"\"\"$F%F%*&,$\"\"#!\"\"F%%\"
>GF%" }{TEXT 336 3 "  ?" }}{PARA 0 "" 0 "" {TEXT 266 4 "a)  " }
{XPPEDIT 256 0 "Pi/6;" "6#*&%#PiG\"\"\"\"\"'!\"\"" }{TEXT 257 4 "    \+
" }{TEXT 343 16 "                " }{TEXT 522 2 "b)" }{TEXT 523 2 "  \+
" }{XPPEDIT 256 0 "Pi/4;" "6#*&%#PiG\"\"\"\"\"%!\"\"" }{TEXT 458 1 " \+
" }{TEXT 344 21 "                 c)  " }{XPPEDIT 256 0 "Pi/3;" "6#*&%
#PiG\"\"\"\"\"$!\"\"" }{TEXT 345 22 "                      " }{TEXT 
528 3 "d) " }{TEXT 529 1 " " }{XPPEDIT 256 0 "Pi/2;" "6#*&%#PiG\"\"\"
\"\"#!\"\"" }{TEXT 460 23 "                       " }{TEXT 536 2 "e)" 
}{TEXT 537 3 "   " }{XPPEDIT 256 0 "3*Pi/4;" "6#*(\"\"$\"\"\"%#PiGF%\"
\"%!\"\"" }{TEXT 459 6 "     \n" }{TEXT 526 2 "f)" }{TEXT 527 2 "  " }
{XPPEDIT 256 0 "arccos(1/7);" "6#-%'arccosG6#*&\"\"\"F'\"\"(!\"\"" }
{TEXT 461 7 "       " }{TEXT 524 2 "g)" }{TEXT 525 2 "  " }{XPPEDIT 
256 0 "arccos(2/7);" "6#-%'arccosG6#*&\"\"#\"\"\"\"\"(!\"\"" }{TEXT 
462 8 "        " }{TEXT 530 2 "h)" }{TEXT 531 2 "  " }{XPPEDIT 256 0 "
arccos(3/7);" "6#-%'arccosG6#*&\"\"$\"\"\"\"\"(!\"\"" }{TEXT 463 6 "  \+
    " }{TEXT 532 3 " i)" }{TEXT 533 2 "  " }{XPPEDIT 256 0 "arccos(4/7
);" "6#-%'arccosG6#*&\"\"%\"\"\"\"\"(!\"\"" }{TEXT 465 7 "       " }
{TEXT 534 2 "j)" }{TEXT 535 2 "  " }{XPPEDIT 256 0 "arccos(5/7);" "6#-
%'arccosG6#*&\"\"&\"\"\"\"\"(!\"\"" }{TEXT 466 6 "      " }{TEXT 464 
2 "  " }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 498 16 
"Answer:    ( c )" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
28 "v := [2,3,1]; w := [3,1,-2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"vG7%\"\"#\"\"$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG7%\"\"
$\"\"\"!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "eqn := cos(t
heta) = dotprod(v,w)/(vectorLength(v)*vectorLength(w)); #cosine of ang
le between v,w" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG/-%$cosG6#%&t
hetaG#\"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "theta \+
= map(arccos, rhs(eqn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&thetaG,
$*&\"\"$!\"\"%#PiG\"\"\"F*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 
{PARA 3 "" 0 "" {TEXT 267 2 " 5" }{TEXT -1 2 ". " }{TEXT 346 34 "What \+
is the radius of the sphere  " }{TEXT 349 1 " " }{XPPEDIT 347 1 "x^2+y
^2+z^2-6*x+5*y-7*z = 17/2;" "6#/,.*$%\"xG\"\"#\"\"\"*$%\"yGF'F(*$%\"zG
F'F(*&\"\"'F(F&F(!\"\"*&\"\"&F(F*F(F(*&\"\"(F(F,F(F/*&\"#<F(F'F/" }
{TEXT 348 2 " ?" }}{PARA 261 "" 0 "" {TEXT -1 50 "a) 1       b) 2     \+
  c) 3        d) 4        e) 5" }}{PARA 261 "" 0 "" {TEXT -1 53 "f)  6
       g) 7       h) 8        i) 9         j) 10" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
499 16 "Answer:    ( f )" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 38 "eqn := x^2+y^2+z^2-6*x+5*y-7*z = 17/2;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%$eqnG/,.*$)%\"xG\"\"#\"\"\"F+*$)%\"yGF*F+F+*$)
%\"zGF*F+F+*&\"\"'F+F)F+!\"\"*&\"\"&F+F.F+F+*&\"\"(F+F1F+F4#\"#<F*" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "eqn := student[completesqua
re](eqn,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG/,.*$),&%\"xG\"
\"\"\"\"$!\"\"\"\"#F+F+\"\"*F-*$)%\"yGF.F+F+*$)%\"zGF.F+F+*&\"\"&F+F2F
+F+*&\"\"(F+F5F+F-#\"#<F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
38 "eqn := student[completesquare](eqn,y);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$eqnG/,,*$),&%\"yG\"\"\"#\"\"&\"\"#F+F.F+F+#\"#h\"\"%
!\"\"*$),&%\"xGF+\"\"$F2F.F+F+*$)%\"zGF.F+F+*&\"\"(F+F:F+F2#\"#<F." }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "eqn := student[completesqua
re](eqn,z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG/,**$),&%\"zG\"
\"\"#\"\"(\"\"#!\"\"F.F+F+#\"#bF.F/*$),&%\"yGF+#\"\"&F.F+F.F+F+*$),&%
\"xGF+\"\"$F/F.F+F+#\"#<F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
22 "map(z -> z+53/2, eqn);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*$),&
%\"zG\"\"\"#\"\"(\"\"#!\"\"F,F)F)*$),&%\"yGF)#\"\"&F,F)F,F)F)*$),&%\"x
GF)\"\"$F-F,F)F)\"#O" }}}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 
264 18 "6. Suppose that   " }{XPPEDIT 539 0 "w = lambda*v;" "6#/%\"wG*
&%'lambdaG\"\"\"%\"vGF'" }{TEXT 538 7 "   and " }{TEXT 358 2 "  " }
{XPPEDIT 259 1 "v;" "6#%\"vG" }{TEXT 350 1 " " }{TEXT 359 29 " is the \+
vector projection of " }{TEXT 360 2 "  " }{XPPEDIT 351 1 "`<`*3,4,1*`>
`;" "6%*&%\"<G\"\"\"\"\"$F%\"\"%*&F%F%%\">GF%" }{TEXT 352 2 "  " }
{TEXT 361 3 " on" }{TEXT 362 3 "   " }{XPPEDIT 353 1 "w = `<`*1,4,8*`>
`;" "6%/%\"wG*&%\"<G\"\"\"F'F'\"\"%*&\"\")F'%\">GF'" }{TEXT 354 1 " " 
}{TEXT 363 10 ". \nWhat is" }{TEXT 364 1 " " }{TEXT 356 1 " " }
{XPPEDIT 357 0 "lambda;" "6#%'lambdaG" }{TEXT 355 2 " ?" }}{PARA 0 "" 
0 "" {TEXT 265 128 "a)  -5        b)  -4         c) -3          d) -2 \+
      e) -1 \n\n f)  0         g) 1           h) 2            i) 3    \+
      j) 4" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT 500 16 "Answer:    ( i )" }{TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
13 "w := [1,4,8];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG7%\"\"\"\"
\"%\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "v = vectorProje
ction([3,4,1],w);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"vG7%#\"\"\"\"
\"$#\"\"%F(#\"\")F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 381 
8 "7.  If  " }{XPPEDIT 373 1 "`<`*a,b,c*`>`" "6%*&%\"<G\"\"\"%\"aGF%%
\"bG*&%\"cGF%%\">GF%" }{TEXT 374 1 " " }{TEXT 566 20 "is the cross pro
duct" }{TEXT 379 1 " " }{XPPEDIT 377 1 "`<`*2,2,1*`>`;" "6%*&%\"<G\"\"
\"\"\"#F%F&*&F%F%%\">GF%" }{TEXT 378 1 " " }{TEXT 380 2 "  " }{TEXT 
375 1 "X" }{TEXT 376 1 " " }{TEXT 370 1 " " }{XPPEDIT 365 1 "`<`*2,1,-
2*`>`;" "6%*&%\"<G\"\"\"\"\"#F%F%,$*&F&F%%\">GF%!\"\"" }{TEXT 366 1 " \+
" }{TEXT 371 15 ",  then what is" }{TEXT 372 1 " " }{TEXT 368 1 " " }
{XPPEDIT 369 0 "a+b+c" "6#,(%\"aG\"\"\"%\"bGF%%\"cGF%" }{TEXT 367 2 " \+
?" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 382 128 "a)  -5        b)  -4         c) -3          d) -2      \+
 e) -1 \n\n f)  0         g) 1           h) 2            i) 3         \+
 j) 4" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 501 16 "Answ
er:    ( e )" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "crossProduct := crossprod(vector([2
,2,1]), vector([2,1,-2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-cross
ProductG-%'vectorG6#7%!\"&\"\"'!\"#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 48 "crossProduct[1]+crossProduct[2]+crossProduct[3];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{SECT 0 {PARA 3 "" 0 "" {TEXT 268 17 "8. Suppose that  " }{XPPEDIT 
472 0 "u;" "6#%\"uG" }{TEXT 467 7 "  and  " }{XPPEDIT 473 0 "v;" "6#%
\"vG" }{TEXT 468 36 "  are vectors.  The magnitudes of   " }{TEXT 558 
1 "u" }{TEXT 559 8 "   and  " }{TEXT 560 1 "v" }{TEXT 561 75 "   are  \+
 2  and  5  respectively.  \nThe dot product of   u   and  v   is   " 
}{TEXT 562 1 "-" }{TEXT 563 37 " 6.     What is the magnitude  of    \+
" }{XPPEDIT 474 0 "u" "6#%\"uG" }{TEXT 471 2 "  " }{TEXT 469 3 "x  " }
{XPPEDIT 475 0 "v;" "6#%\"vG" }{TEXT 470 6 "  ?   " }}{PARA 258 "" 0 "
" {TEXT 383 5 "\na)  " }{XPPEDIT 384 1 "1;" "6#\"\"\"" }{TEXT 385 10 "
      b)  " }{XPPEDIT 386 1 "2;" "6#\"\"#" }{TEXT 387 10 "      c)  " 
}{XPPEDIT 388 1 "3;" "6#\"\"$" }{TEXT 389 10 "       d) " }{XPPEDIT 
390 1 "4;" "6#\"\"%" }{TEXT 391 10 "      e)  " }{XPPEDIT 392 1 "5;" "
6#\"\"&" }{TEXT 393 10 "    \n f)  " }{XPPEDIT 394 1 "6;" "6#\"\"'" }
{TEXT 395 10 "      g)  " }{XPPEDIT 396 1 "7;" "6#\"\"(" }{TEXT 397 
10 "      h)  " }{XPPEDIT 398 1 "8;" "6#\"\")" }{TEXT 399 9 "      i) \+
" }{XPPEDIT 400 1 "9;" "6#\"\"*" }{TEXT 401 57 "        j) Insufficien
t information to determine answer  " }{TEXT -1 1 " " }}{PARA 3 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 510 16 "Answer:    ( h )" }
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 5 "Let  " }{XPPEDIT 18 0 "theta;" "6#%&thetaG" }{TEXT -1 25 "  be t
he angle between   " }{TEXT 564 1 "u" }{TEXT -1 7 "   and " }{TEXT 
565 3 "  v" }{TEXT -1 12 " .   Then   " }{XPPEDIT 18 0 "-6 = abs(u)*ab
s(v)*cos(theta);" "6#/,$\"\"'!\"\"*(-%$absG6#%\"uG\"\"\"-F)6#%\"vGF,-%
$cosG6#%&thetaGF," }{TEXT -1 3 ".  " }}{PARA 0 "" 0 "" {TEXT -1 1 " " 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 53 "cos(theta) = solve( -6 = 2*5*cos(theta), cos(theta));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/-%$cosG6#%&thetaG#!\"$\"\"&" }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "Since,  " }{XPPEDIT 
18 0 "sin(theta) = sqrt(1-cos(theta)^2);" "6#/-%$sinG6#%&thetaG-%%sqrt
G6#,&\"\"\"F,*$-%$cosG6#F'\"\"#!\"\"" }{TEXT -1 9 ", we have" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "sin(theta) = sqrt(1 - (-3/5)^2);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$sinG6#%&thetaG#\"\"%\"\"&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "2*5*4/5;  #Required magnitud
e" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 269 37 "9. Wh
at is the area of parallelogram " }{TEXT 402 4 "PQRS" }{TEXT 403 4 " i
f " }{TEXT 404 1 "P" }{TEXT 405 12 " = (4,3,5), " }{TEXT 406 1 "Q" }
{TEXT 407 13 " = (5,5,6),  " }{TEXT 408 1 "R" }{TEXT 409 27 " = (6,7,8
), and S =(5,5,7)?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 277 24 "a)  1              b)   " }{XPPEDIT 278 0 "sqrt(2);" "6#
-%%sqrtG6#\"\"#" }{TEXT 279 18 "             c)   " }{XPPEDIT 280 0 "s
qrt(3);" "6#-%%sqrtG6#\"\"$" }{TEXT 281 19 "              d)   " }
{XPPEDIT 282 0 "2;" "6#\"\"#" }{TEXT 283 21 "                 e)  " }
{XPPEDIT 284 0 "sqrt(5);" "6#-%%sqrtG6#\"\"&" }{TEXT 285 21 "         \+
      \nf)   " }{XPPEDIT 286 0 "sqrt(6);" "6#-%%sqrtG6#\"\"'" }{TEXT 
287 14 "          g)  " }{XPPEDIT 288 0 "2*sqrt(2);" "6#*&\"\"#\"\"\"-
%%sqrtG6#F$F%" }{TEXT 289 17 "            h)   " }{XPPEDIT 290 0 "3;" 
"6#\"\"$" }{TEXT 291 21 "                 i)  " }{XPPEDIT 292 0 "2*sqr
t(3);" "6#*&\"\"#\"\"\"-%%sqrtG6#\"\"$F%" }{TEXT 293 18 "             \+
j)   " }{XPPEDIT 294 0 "3*sqrt(2);" "6#*&\"\"$\"\"\"-%%sqrtG6#\"\"#F%
" }}{PARA 0 "" 0 "" {TEXT 295 1 " " }}{PARA 0 "" 0 "" {TEXT 511 16 "An
swer:    ( e )" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
49 "u := vector([5-4,5-3,6-5]);   #vector from P to Q" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"uG-%'vectorG6#7%\"\"\"\"\"#F)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "v := vector([6-5,7-5,8-6]);   #Q to
 R" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG-%'vectorG6#7%\"\"\"\"\"#F
*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "w := crossprod(u,v);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG-%'vectorG6#7%\"\"#!\"\"\"\"!
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "vectorLength(evalm(w));
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$\"\"&#\"\"\"\"\"#" }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 270 76 "10.   Wh
at is the volume of the parallelepiped formed from the three vectors" 
}{TEXT 416 1 " " }{XPPEDIT 410 1 "`<`*2,2,4*`>`;" "6%*&%\"<G\"\"\"\"\"
#F%F&*&\"\"%F%%\">GF%" }{TEXT 411 3 ",  " }{XPPEDIT 412 1 "`<`*2,1,1*`
>` " "6%*&%\"<G\"\"\"\"\"#F%F%*&F%F%%\">GF%" }{TEXT 413 3 ",  " }
{TEXT 418 3 "and" }{TEXT 419 2 "  " }{XPPEDIT 414 1 "`<`*1,2,3*`>` " "
6%*&%\"<G\"\"\"F%F%\"\"#*&\"\"$F%%\">GF%" }{TEXT 415 1 "?" }{TEXT 417 
3 " \n\n" }{TEXT 276 70 "a)  1           b)  2             c)   3     \+
    d)  4           e)  5" }{TEXT 420 21 "                     " }}
{PARA 0 "" 0 "" {TEXT 422 34 "f)  6            g)  7            " }
{TEXT -1 1 " " }{TEXT 567 2 "h)" }{TEXT 421 36 "  8           i) 9    \+
        j)  12" }{TEXT -1 2 "  " }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 509 16 "Answer:    ( d )" }{TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "u := vector([2,2,4]);\nv := \+
vector([2,1,1]);\nw := vector([1,2,3]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"uG-%'vectorG6#7%\"\"#F)\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"vG-%'vectorG6#7%\"\"#\"\"\"F*" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"wG-%'vectorG6#7%\"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 31 "abs(dotprod(u,crossprod(v,w)));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#\"\"%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 
"" 0 "" {TEXT 569 203 "11.  The line with parametric equations   x = 1
 + 2t,   y = 3t,   z = 2 - t   intersects the line  with parametric eq
uations   x = 9 + 2t,   y = 5 - 4t,   z = 1 + 2t   in a point  (a,b,c)
.   What is  b ?" }}{PARA 0 "" 0 "" {TEXT 588 70 "a)  1           b)  \+
2             c)   3         d)  4           e)  5" }{TEXT 589 22 "   \+
                  \n" }{TEXT 591 34 "f)  6            g)  7           \+
 " }{TEXT -1 1 " " }{TEXT 592 2 "h)" }{TEXT 590 36 "  8           i) 9
            j)  12" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 593 12 "Answer (
 i )" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "line[1] := [x = 1 + 2*t,   y = 3*t,   z = 2 - t];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%lineG6#\"\"\"7%/%\"xG,&F'F'*&\"\"#
F'%\"tGF'F'/%\"yG,$*&\"\"$F'F.F'F'/%\"zG,&F-F'F.!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "line[2] := [x = 9 + 2*s,   y = 5 - \+
4*s,   z = 1 + 2*s ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%lineG6#\"
\"#7%/%\"xG,&\"\"*\"\"\"*&F'F-%\"sGF-F-/%\"yG,&\"\"&F-*&\"\"%F-F/F-!\"
\"/%\"zG,&F-F-*&F'F-F/F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
73 "for j from 1 to 3 do\neqn[j] := rhs(line[1][j]) = rhs(line[2][j]);
\nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$eqnG6#\"\"\"/,&F'F'*&
\"\"#F'%\"tGF'F',&\"\"*F'*&F+F'%\"sGF'F'" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>&%$eqnG6#\"\"#/,$*&\"\"$\"\"\"%\"tGF,F,,&\"\"&F,*&\"\"%F,%\"sGF
,!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$eqnG6#\"\"$/,&\"\"#\"\"
\"%\"tG!\"\",&F+F+*&F*F+%\"sGF+F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "parameterSolns := solve(\{eqn[1],eqn[2]\},\{s,t\});" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/parameterSolnsG<$/%\"sG!\"\"/%\"t
G\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "subs(parameterSol
ns,eqn[3] );  #Verification that last coordinate works out" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/!\"\"F$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "subs(parameterSolns,[seq(rhs(line[1][j]),j=1..3)]);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"(\"\"*!\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 51 "subs(parameterSolns,[seq(rhs(line[2][j]),
j=1..3)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"(\"\"*!\"\"" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 " " }
{TEXT 271 105 "12. The line through the points ( 4, -1, -2) and (6, 3,
 -1)  intersects the plane y = 11  at the point  (" }{TEXT 429 1 "a" }
{TEXT 430 2 ", " }{TEXT 431 1 "b" }{TEXT 432 24 ", c). \n        What \+
is  " }{TEXT 427 5 "a + c" }{TEXT 428 78 " ? \n\na)  8            b)  \+
9             c)  10         d)  11           e)  12" }{TEXT 424 21 " \+
                    " }}{PARA 0 "" 0 "" {TEXT 425 33 "f)   13         \+
g)   14          " }{TEXT -1 1 " " }{TEXT 426 37 "h)   15        i) 16
             j)  " }{TEXT 587 2 "17" }}{PARA 3 "" 0 "" {TEXT 423 1 " \+
" }}{PARA 0 "" 0 "" {TEXT 508 16 "Answer:    ( d )" }{TEXT -1 0 "" }}
{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "eq
n1 := x = 4 + t*(4-6); \neqn2 := y = -1 + t*(-1-3);\neqn3 := z = -2 + \+
t*(-2-(-1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn1G/%\"xG,&\"\"%
\"\"\"*&\"\"#F)%\"tGF)!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn2
G/%\"yG,&\"\"\"!\"\"*&\"\"%F(%\"tGF(F)" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%%eqn3G/%\"zG,&\"\"#!\"\"%\"tGF)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "eqn4 := subs(y=11,eqn2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%eqn4G/\"#6,&\"\"\"!\"\"*&\"\"%F(%\"tGF(F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "eqn5 := t = solve(eqn4, t);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn5G/%\"tG!\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "rhs(subs(eqn5,eqn1))+rhs(subs(eqn5,
eqn3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#6" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 
"" {TEXT 272 1 " " }{TEXT 437 17 "13.  The vector  " }{TEXT 433 1 "<" 
}{TEXT 434 11 " a , b , 2 " }{TEXT 435 1 ">" }{TEXT 436 69 "  is perpe
ndicular to the plane  z  =  2x  - 3y  +  1.   What is a ? " }{TEXT 
438 3 " \n\n" }{TEXT 439 132 "a) -4          b) - 3         c) - 2    \+
    d) - 1         e) 0  \nf)   1          g)   2         h)  3       \+
   i)  4          j)  5" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 507 16 "Answer:    ( a )" }
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "eqn1 := a = k*2;  \+
eqn2 := b = k*(-3);    eqn3 := 2 = k*(-1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%eqn1G/%\"aG,$*&\"\"#\"\"\"%\"kGF*F*" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%%eqn2G/%\"bG,$*&\"\"$\"\"\"%\"kGF*!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn3G/\"\"#,$%\"kG!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "subs(k=-2,eqn1);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#/%\"aG!\"%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 
{PARA 261 "" 0 "" {TEXT -1 84 "14. A plane passes through the three po
ints  (1, 0, 0),  (0, 4, 0),  and (2, 3, 2). " }}{PARA 3 "" 0 "" 
{TEXT 440 50 "Its equation is   Ax + y + Cz = D.   What is   A? " }
{TEXT 442 1 "\n" }}{PARA 3 "" 0 "" {TEXT 441 107 "a) 1         b) 2   \+
    c) 3      d) 4      e) 5      f)   6      g)   7      h)  8      i
)  9      j) 10  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 506 16 "Answer:    ( d )" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 9 "Method 1:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 56 "u := vector([1-0,0-4,0-0]);  v := vector([0-2,
4-3,0-2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG-%'vectorG6#7%\"\"
\"!\"%\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG-%'vectorG6#7%!\"
#\"\"\"F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "w := crossprod
(u,v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG-%'vectorG6#7%\"\")\"
\"#!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "A = (1/2)*w[1];
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"AG\"\"%" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 9 "Method 2:" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "eqn1 := s
ubs( \{x=1,y=0,z=0\} , A*x + y + C*z = D );" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%eqn1G/%\"AG%\"DG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "eqn2 := subs( \{x=0,y=4,z=0\} , A*x + y + C*z = D );
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn2G/\"\"%%\"DG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "eqn3 := subs( \{x=2,y=3,z=2\} , A*x
 + y + C*z = D );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn3G/,(*&\"\"
#\"\"\"%\"AGF)F)\"\"$F)*&F(F)%\"CGF)F)%\"DG" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 32 "solve(\{eqn1,eqn2,eqn3\},\{A,C,D\});" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#<%/%\"AG\"\"%/%\"CG#!\"(\"\"#/%\"DGF&" }}}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 
{PARA 3 "" 0 "" {TEXT 445 168 "15. A plane is perpendicular to the lin
e   2 - x  =  (2y + 2)/6  =  2z . The plane passes through the point (
1, -2,- 1) as well as the point ( a, -4, 3 ).  What is  a ?" }{TEXT 
446 3 "  \n" }{TEXT 444 131 "\na) -3          b) - 2         c) - 1   \+
     d)  0         e) 1  \nf)   2          g)   3         h)  4       \+
   i)  5          j)  " }{TEXT 443 2 "6\n" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT 505 16 "Answer:    ( a )" }{TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
52 "eqn := (-1)*(x-1) + 3*(y-(-2)) + (1/2)*(z-(-1)) = 0;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%$eqnG/,*%\"xG!\"\"#\"#:\"\"#\"\"\"*&\"\"$F,%\"
yGF,F,*&F+F(%\"zGF,F,\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
42 "eqn2 := subs( \{x = a, y=-4, z=3 \} , eqn );" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%eqn2G/,&%\"aG!\"\"\"\"$F(\"\"!" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 15 "solve(eqn2, a);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#!\"$" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "
" {TEXT 262 109 "16.  The two planes  x + y + 2z = 1  and  x - y + 4z \+
= 5  intersect in a line that is parallel to the \nvector" }{TEXT 454 
2 "  " }{TEXT 449 1 "<" }{TEXT 450 12 " a , b , -1 " }{TEXT 451 1 ">" 
}{TEXT 452 18 ".   What is   a ? " }{TEXT 453 3 " \n\n" }{TEXT 448 
132 "a) -4          b) - 3         c) - 2        d) - 1         e) 0  \+
\nf)   1          g)   2         h)  3          i)  4          j)  5" 
}{TEXT 447 1 "\n" }}{PARA 0 "" 0 "" {TEXT 504 16 "Answer:    ( h )" }
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "v := crossprod(vec
tor([1,1,2]),vector([1,-1,4]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"vG-%'vectorG6#7%\"\"'!\"#F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 22 "scalarmul(v , (1/2) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vec
torG6#7%\"\"$!\"\"F(" }}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}}{SECT 0 {PARA 261 "" 0 "" {TEXT -1 164 "17. A plan
e is parallel to the plane x + 2y - 3z = 0 and also passes through the
 point (10, 1, 2). What is the sum of its three intercepts with the co
ordinate axes?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" 
{TEXT -1 161 "a)  6            b)  7          c)  8               d)  \+
9            e) 12              \nf)  16           g) 18         h)  2
0             i)  22           j) 24" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT 503 16 "Answer:    ( b )" }{TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "eq
n := x + 2*y - 3*z = D;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG/,(%
\"xG\"\"\"*&\"\"#F(%\"yGF(F(*&\"\"$F(%\"zGF(!\"\"%\"DG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "eqn2 := subs(\{x=10,y=1,z=2\},eqn);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn2G/\"\"'%\"DG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "eqn := subs(D=lhs(eqn2),eqn);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG/,(%\"xG\"\"\"*&\"\"#F(%\"yGF(F
(*&\"\"$F(%\"zGF(!\"\"\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
19 "6/1+(6/2)+(6/(-3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"(" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 
{PARA 261 "" 0 "" {TEXT -1 48 "18.  What might the equation of this su
rface be?" }}{PARA 261 "" 0 "" {TEXT -1 19 "                   " }
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