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" }{TEXT 342 6 "If " }{XPPEDIT 363 1 "u=`<`*a,b,c*`>`" "6%/%\"uG*&%\"GF'" }{TEXT 563 8 " and " }{TEXT -1 1 " \+ " }{XPPEDIT 364 1 "v=`<`*d,e,1*`>`" "6%/%\"vG*&%\"GF'" }{TEXT 339 63 " are parallel vectors then which one or two of the following " }{TEXT 340 4 "must" }{TEXT 341 20 " be true? \n\nI) " }{XPPEDIT 565 1 "u=lambda*v" "/%\"uG*&%'lambdaG\"\"\"%\" vGF&" }{TEXT 566 21 " for some scalar " }{XPPEDIT 564 1 "lambda" " I'lambdaG6\"" }{TEXT 574 8 " \nII) " }{XPPEDIT 568 1 "u" "I\"uG6\"" }{TEXT 575 1 " " }{TEXT 569 1 "X" }{TEXT 576 2 " " }{XPPEDIT 567 1 "v =0" "/%\"vG\"\"!" }{TEXT 577 13 " \nIII) " }{XPPEDIT 571 1 "u" " I\"uG6\"" }{TEXT 572 1 "." }{XPPEDIT 570 1 "v=0" "/%\"vG\"\"!" }{TEXT 578 7 "\nIV) " }{XPPEDIT 573 1 "b=c*e" "/%\"bG*&%\"cG\"\"\"%\"eGF&" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT -1 95 "a) I \+ only \nb) II only \nc) III only \nd) IV only \ne) I, \+ II only \nf) I, III only " }}{PARA 258 "" 0 "" {TEXT 343 80 "g) I,IV o nly \nh) II, III only \ni) II, IV only \nj) III, IV o nly " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 263 "" 0 "" {TEXT 298 4 "2. " }{TEXT -1 29 "If the magnitude of vector " }{XPPEDIT 19 1 "v=`<`*1,b,-2*`>`" "6%/%\"vG*&%\" GF'!\"\"" }{TEXT -1 27 " is 3 then what is " }{XPPEDIT 19 1 "b " "I\"bG6\"" }{TEXT -1 2 "? " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT 344 4 "a) " }{XPPEDIT 345 1 "0" "\"\"!" }{TEXT 346 9 " b) " }{XPPEDIT 347 1 "1" "\"\"\"" }{TEXT 348 10 " c) " }{XPPEDIT 349 1 "-1" ",$\"\"\"!\"\"" }{TEXT 350 7 " d) " }{XPPEDIT 351 1 "2" "\"\"#" }{TEXT 352 10 " e) " }{XPPEDIT 353 1 "-2" ",$ \"\"#!\"\"" }{TEXT 354 11 " f) " }{XPPEDIT 355 1 "3" "\"\"$" } {TEXT 356 11 " g) " }{XPPEDIT 357 1 "-3" ",$\"\"$!\"\"" }{TEXT 358 8 " h) " }{XPPEDIT 359 1 "4" "\"\"%" }{TEXT 360 8 " i) " } {XPPEDIT 361 1 "-4" ",$\"\"%!\"\"" }{TEXT 362 76 " \+ \nj) Insufficient information to determine answer " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 262 18 "3. If the vectors " }{TEXT 369 2 " " }{XPPEDIT 372 1 "`<`*0,2,b*` >`" "6%*&%\"GF%" }{TEXT 366 1 " " } {TEXT 370 3 "and" }{TEXT 371 2 " " }{XPPEDIT 373 1 "`<`*2,-1,-2*`>`" "6%*&%\"GF%F(" }{TEXT 367 1 " " } {TEXT 374 29 " are perpendicular then what " }{TEXT 375 2 "is" }{TEXT 588 1 " " }{XPPEDIT 376 1 "b" "I\"bG6\"" }{TEXT 368 1 " " }{TEXT 377 2 "? " }{TEXT 378 2 " " }}{PARA 3 "" 0 "" {TEXT 297 154 "a) -1 \+ b) -1/2 c) 0 d) 1/2 e) 1 \nf ) 3/2 g) 2 h) 5/2 i) 3 j) 7 /2 " }{TEXT 379 7 " \n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 263 1 " " } {TEXT 386 36 "4. What is the angle between vectors" }{TEXT 387 3 " \+ " }{XPPEDIT 384 1 "`<`*1,2,2*`>`" "6%*&%\"G F%" }{TEXT 380 1 " " }{TEXT 382 3 "and" }{TEXT 383 2 " " }{XPPEDIT 385 1 "`<`*`3/5`,`4/5`,0*`>`" "6%*&%\"GF%" }{TEXT 381 3 " ?" }}{PARA 0 "" 0 "" {TEXT 269 4 "a) " } {XPPEDIT 256 0 "Pi/6" "*&%#PiG\"\"\"\"\"'!\"\"" }{TEXT 257 11 " \+ " }{TEXT 388 3 "b) " }{TEXT 389 1 " " }{XPPEDIT 303 0 "Pi/4" "*&%# PiG\"\"\"\"\"%!\"\"" }{TEXT 304 14 " c) " }{XPPEDIT 305 0 "P i/3" "*&%#PiG\"\"\"\"\"$!\"\"" }{TEXT 306 7 " " }{TEXT 390 5 " \+ d) " }{XPPEDIT 307 0 "Pi/2" "*&%#PiG\"\"\"\"\"#!\"\"" }{TEXT 308 5 " \+ " }{TEXT 391 6 " e)" }{TEXT 392 2 " " }{XPPEDIT 579 0 "arcsin(2 /5)" "-%'arcsinG6#*&\"\"#\"\"\"\"\"&!\"\"" }{TEXT 580 3 " " }{TEXT 311 2 " " }}{PARA 262 "" 0 "" {TEXT 261 4 "f) " }{TEXT 258 2 " " } {XPPEDIT 309 0 "arcsin(11/25)" "-%'arcsinG6#*&\"#6\"\"\"\"#D!\"\"" } {TEXT 310 8 " g) " }{XPPEDIT 312 0 "arcsin(7/25)" "-%'arcsinG6#*& \"\"(\"\"\"\"#D!\"\"" }{TEXT 313 9 " h) " }{XPPEDIT 314 0 "arccos (2/5)" "-%'arccosG6#*&\"\"#\"\"\"\"\"&!\"\"" }{TEXT 315 8 " i) " } {XPPEDIT 316 0 "arccos(11/25)" "-%'arccosG6#*&\"#6\"\"\"\"#D!\"\"" } {TEXT 259 7 " j) " }{XPPEDIT 318 0 "arccos(7/25" "-%'arccosG6#*&\" \"(\"\"\"\"#D!\"\"" }{TEXT 319 1 " " }{TEXT 317 2 " " }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 270 2 " 5" }{TEXT -1 2 ". " }{TEXT 393 34 "What is the radius of the sphere " }{TEXT 396 1 " " }{XPPEDIT 394 1 "2*x^2+2*y^2+2*z^2+4*y+1=0" "/,,*&\"\"#\"\"\"*$%\"x GF%F&F&*&F%F&*$%\"yGF%F&F&*&F%F&*$%\"zGF%F&F&*&\"\"%F&F+F&F&F&F&\"\"! " }{TEXT 395 2 " ?" }}{PARA 261 "" 0 "" {TEXT -1 58 "a) 1/2 b) 1 c) 3/2 d) 2 e) 5/2" }}{PARA 265 "" 0 "" {TEXT -1 59 "f) 3 g) 7/2 h) 4 i) 9/2 j) 5" }} {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 3 "" 0 "" {TEXT -1 1 " " }{TEXT 266 43 "6. What is the length of the projection of " }{TEXT 402 2 " " }{XPPEDIT 397 1 "`<`*1,-1,1*`>` " "6%*&%\"GF%" }{TEXT 398 2 " " } {TEXT 403 3 " on" }{TEXT 404 3 " " }{XPPEDIT 399 1 "`<`*2,1,-2*`>`" "6%*&%\"GF%!\"\"" }{TEXT 400 2 " ?" }} {PARA 0 "" 0 "" {TEXT 267 142 "\na) 1/9 b) 2/9 c) 1/3 d) 4/9 e) 5/9 \n\n f) 2/3 g) 7/9 h) 8/9 i) 1 j) 1/6" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 268 8 "7. Let " }{TEXT 421 1 " " }{XPPEDIT 405 1 "P" "I\"PG6\"" }{TEXT 406 1 " " }{TEXT 410 38 " be the plane that contains the lines " }{TEXT 584 25 "x = 1+2t, \+ y=3t, z = -t" }{TEXT 585 9 " and " }{TEXT 586 26 "x = 2t, y=1+ 3t, z = 1-t" }{TEXT 587 7 " . Let " }{TEXT 414 1 " " }{XPPEDIT 419 1 "Q=`<`*8,b,c*`>`" "6%/%\"QG*&%\"GF'" }{TEXT 420 1 " " }{TEXT 415 37 " be a vector that is perpendicular to " }{TEXT 422 2 " " }{XPPEDIT 416 1 "P" "I\"PG6\"" }{TEXT 417 11 " . \+ What is" }{TEXT 412 1 " " }{TEXT 408 1 " " }{XPPEDIT 409 0 "b" "I\"bG6 \"" }{TEXT 407 2 " ?" }{TEXT 413 1 "\n" }}{PARA 0 "" 0 "" {TEXT 423 128 "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 "" }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 438 28 "8. The vector c ross product" }{TEXT 436 1 " " }{XPPEDIT 434 1 "`<`*1,-1,1*`>` " "6%*& %\"GF%" }{TEXT 435 1 " " }{TEXT 437 2 " " }{TEXT 432 1 "X" }{TEXT 433 1 " " }{TEXT 429 1 " " }{XPPEDIT 424 1 "`<`*2,b,c*`>`" "6%*&%\"GF%" } {TEXT 425 1 " " }{TEXT 430 16 " is parallel to " }{TEXT 582 1 " " } {XPPEDIT 581 1 "`<`*2,3,2*`>`" "6%*&%\"G F%" }{TEXT 583 9 ". What is" }{TEXT 431 1 " " }{TEXT 427 1 " " } {XPPEDIT 428 0 "b" "I\"bG6\"" }{TEXT 426 2 " ?" }{TEXT -1 1 " " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 439 234 "a) -5 \+ b) -4 c) -3 d) -2 e) -1 \n\nf) 0 \+ g) 1 h) 2 \ni) No such b is possible \+ \nj) Such a b exists but not enough information has been given to de termine it uniquely. " }}{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 3 "" 0 "" {TEXT 271 54 "9. What is the \+ sine of the angle between the vectors " }{XPPEDIT 440 1 "`<`*1,-1,1*` >` " "6%*&%\"GF%" }{TEXT 441 7 " and \+ " }{XPPEDIT 442 1 "`<`*1,1,3*`>` " "6%*&%\" GF%" }{TEXT 443 2 " ?" }{TEXT 444 1 " " }}{PARA 258 "" 0 "" {TEXT 445 5 "\na) " }{XPPEDIT 446 1 "1/6" "*&\"\"\"F#\"\"'!\"\"" }{TEXT 447 9 " b) " }{XPPEDIT 448 1 "1/3" "*&\"\"\"F#\"\"$!\"\"" }{TEXT 449 10 " c) " }{XPPEDIT 450 1 "2/3" "*&\"\"#\"\"\"\"\"$!\"\"" }{TEXT 451 7 " d) " }{XPPEDIT 452 1 "sqrt(2)/11" "*&-%%sqrtG6#\"\"#\"\"\" \"#6!\"\"" }{TEXT 453 10 " e) " }{XPPEDIT 454 1 "2*sqrt(2)/11" " *(\"\"#\"\"\"-%%sqrtG6#F#F$\"#6!\"\"" }{TEXT 455 9 " f) " } {XPPEDIT 456 1 "sqrt(5)/11" "*&-%%sqrtG6#\"\"&\"\"\"\"#6!\"\"" }{TEXT 457 11 " g) " }{XPPEDIT 458 1 "sqrt(3)/11" "*&-%%sqrtG6#\"\"$\" \"\"\"#6!\"\"" }{TEXT 459 8 " h) " }{XPPEDIT 460 1 "sqrt(3)/6" "*& -%%sqrtG6#\"\"$\"\"\"\"\"'!\"\"" }{TEXT 461 8 " i) " }{XPPEDIT 462 1 "sqrt(3)/9" "*&-%%sqrtG6#\"\"$\"\"\"\"\"*!\"\"" }{TEXT 463 76 " \+ \nj) Insufficient information to determine an swer " }{TEXT -1 1 " " }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 274 82 "10. The line through the points ( 0, -1, 2) and (1, 2, 5) passes through a point (" }{TEXT 492 1 "a" }{TEXT 493 2 ", " }{TEXT 494 1 "b" }{TEXT 495 15 ", 8). What is " }{TEXT 490 1 "a" }{TEXT 491 5 " ? \n\n" }}{PARA 3 "" 0 "" {TEXT 486 74 "a) -4 b) -3 c) -2 d) \+ -1 e) 0" }{TEXT 487 21 " " }}{PARA 0 " " 0 "" {TEXT 488 36 "f) 1 g) 2 " }{TEXT -1 1 " " }{TEXT 489 39 "h) 3 i) 4 j) " }{TEXT -1 1 " " }{TEXT 496 1 "5" }{TEXT -1 2 " " }}{PARA 3 "" 0 "" {TEXT 485 1 " " }}{PARA 3 "" 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 3 "" 0 "" {TEXT 275 1 " " }{TEXT 501 17 "11. The vect or " }{TEXT 497 1 "<" }{TEXT 498 12 " a , b , -2 " }{TEXT 499 1 ">" } {TEXT 500 68 " is perpendicular to the plane x + y + 2z = 0. \+ What is a ? " }{TEXT 502 3 " \n\n" }{TEXT 503 132 "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 -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 266 "" 0 "" {TEXT -1 84 "12. A plane passes through the three points (1, 0, 0), (1, 1, 0), and (0, 0, 2). " }}{PARA 3 "" 0 "" {TEXT 504 50 "Its equation is Ax + By + z = D. What is D? " }{TEXT 507 1 "\n" }}{PARA 3 "" 0 "" {TEXT 506 132 "a) -4 b) - 3 c) - 2 d) - 1 \+ e) 0 \nf) 1 g) 2 h) 3 i) 4 \+ j) 5" }{TEXT 505 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{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 3 "" 0 "" {TEXT 510 154 "13. A pla ne is perpendicular to the line 1 - x = (1/2)y = 2z . The plane pa sses through the point (1, 0, 0). What is the z-intercept of the p lane?" }{TEXT 511 3 " \n" }{TEXT 509 133 "\na) -4 b) - 3 \+ c) - 2 d) - 1 e) 0 \nf) 1 g) 2 \+ h) 3 i) 4 j) 5" }{TEXT 508 1 "\n" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{SECT 0 {PARA 267 "" 0 "" {TEXT -1 162 "14. A plane is parallel to the plane x + y + 2z = 0 and also passes through the p oint (2, 0, 2). What is the sum of its three intercepts with the coord inate axes?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 149 "a) 4 b) 5 c) 6 d) 7 \+ e) 8 \nf) 9 g) 10 h) 11 \+ i) 12 j) 15" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{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 3 "" 0 "" {TEXT -1 1 " " }{TEXT 276 34 "15. The set that is described by \+ " }{XPPEDIT 524 1 "x=0,y>=` `*0" "6$/%\"xG\"\"!1*&%#~~G\"\"\"F%F)%\"y G" }{TEXT 520 107 " in rectangular coordinates is described by which \+ of the following equations in spherical coordinates? " }}{PARA 3 " " 0 "" {TEXT 277 4 "a) " }{XPPEDIT 278 0 "rho=sin(phi)" "/%$rhoG-%$si nG6#%$phiG" }{TEXT 279 17 " b) " }{XPPEDIT 280 0 "rho=2*s in(phi)" "/%$rhoG*&\"\"#\"\"\"-%$sinG6#%$phiGF&" }{TEXT 281 18 " \+ \nc) " }{XPPEDIT 282 0 "rho=cos(phi)" "/%$rhoG-%$cosG6#%$phiG " }{TEXT 283 17 " d) " }{XPPEDIT 284 0 "rho=2*cos(phi)" " /%$rhoG*&\"\"#\"\"\"-%$cosG6#%$phiGF&" }{TEXT 285 17 " \ne) " }{XPPEDIT 286 0 "rho=cos(theta)" "/%$rhoG-%$cosG6#%&thetaG" } {TEXT 287 18 " f) " }{XPPEDIT 288 0 "rho=2*cos(theta)" " /%$rhoG*&\"\"#\"\"\"-%$cosG6#%&thetaGF&" }{TEXT 289 16 " \ng ) " }{XPPEDIT 290 0 "theta=phi" "/%&thetaG%$phiG" }{TEXT 291 27 " \+ h) " }{XPPEDIT 292 0 "phi=Pi/4" "/%$phiG*&%#PiG\" \"\"\"\"%!\"\"" }{TEXT 293 1 " " }{TEXT 530 7 " " }{TEXT 532 7 " \ni) " }{XPPEDIT 294 0 "phi=3*Pi/4" "/%$phiG*(\"\"$\"\"\"%#PiGF&\" \"%!\"\"" }{TEXT 295 24 " j) " }{XPPEDIT 296 0 "th eta=Pi/2" "/%&thetaG*&%#PiG\"\"\"\"\"#!\"\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}}}{MARK "13 0 0" 153 }{VIEWOPTS 1 1 0 1 1 1803 }