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test3review-problems

# test3review-problems - suleimenov(bs26835 test3review...

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suleimenov (bs26835) – test3review – rusin – (55565) 1 This print-out should have 56 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. You know the drill: this doesn’t count, it’s available without answers until Friday evening, and then answers will be available too. Test is Tuesday, 4/19. Good luck! Note: This review probably contains some repeats of homework questions; of course if you are sure you know how to solve a problem you don’t have to spend time working it out! 001 0.0points Find the trace on the xy -plane of the sphere having center at (3 , 1 , 1) and radius 3. 1. x 2 + y 2 6 x + 2 y + 2 = 0 2. y 2 + z 2 + 2 y 2 z + 2 = 0 3. x 2 + y 2 + 6 x 2 y = 2 4. y 2 + z 2 2 y + 2 z = 2 5. x 2 + z 2 6 x 2 z + 2 = 0 6. x 2 + z 2 + 6 x + 2 z = 2 002 0.0points Which of the following sets of inequalitites describes the region consisting of all points outside a sphere of radius 2 centered at the origin and inside a sphere of radius 5 centered at the origin. 1. 4 < x 2 + y 2 + z 2 < 25 2. 2 x 2 + y 2 + z 2 5 3. 4 x 2 + y 2 + z 2 25 4. 2 x 2 + y 2 + z 2 < 5 5. 4 < x 2 + y 2 + z 2 25 6. 2 < x 2 + y 2 + z 2 < 5 003 0.0points When u , v are the displacement vectors u = −−→ AB , v = −→ AP , determined by the parallelogram A B C D P Q R S O express −−→ QC in terms of u and v . 1. −−→ QC = u + 2 v 2. −−→ QC = 2 u 3. −−→ QC = 2 v u 4. −−→ QC = 2( u v ) 5. −−→ QC = 2 v 6. −−→ QC = 2( u + v ) 004 0.0points The parallelopiped in 3-space shown in Q P S C B A D R

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suleimenov (bs26835) – test3review – rusin – (55565) 2 is determined by its vertices P ( 4 , 2 , 4) , Q (1 , 2 , 2) , R ( 2 , 2 , 1) , S ( 5 , 1 , 3) . Find the vector v represented by the directed line segment −−→ PC . 1. v = ( 7 , 8 , 6 ) 2. v = ( 7 , 4 , 5 ) 3. v = ( 0 , 2 , 1 ) 4. v = ( 1 , 7 , 4 ) 5. v = ( 6 , 7 , 6 ) 6. v = ( 4 , 3 , 3 ) 005 0.0points For the vectors u and v shown in u v which of the following is equivalent to u v ? 1. 2. 3. 4. 5. 6. 006 0.0points Determine the length of the vector a + 2 b when a = 3 i + 2 j + k , b = 2 i + j + 2 k .
suleimenov (bs26835) – test3review – rusin – (55565) 3 1. length = 6 2. length = 34 3. length = 38 4. length = 2 10 5. length = 42 007 0.0points Find a unit vector n with the same direction as the vector v = 2 i 6 j + 3 k . 1. n = 2 7 i + 6 7 j 3 7 k 2. n = 2 9 i 2 3 j + 1 3 k 3. n = 2 7 i 6 7 j + 3 7 k 4. n = 1 5 i + 3 5 j 3 10 k 5. n = 2 9 i + 2 3 j 1 3 k 6. n = 1 5 i 3 5 j + 3 10 k 008 0.0points Find the vector projection of b onto a when b = i 4 j + 2 k , a = 3 i + 2 j + 3 k . 1. vector proj. = 22 21 ( i 4 j + 2 k ) 2. vector proj. = 22 21 (3 i + 2 j + 3 k ) 3. vector proj. = 1 21 ( i 4 j + 2 k ) 4. vector proj. = 1 22 ( i 4 j + 2 k ) 5. vector proj. = 1 21 (3 i + 2 j + 3 k ) 6. vector proj. = 1 22 (3 i + 2 j + 3 k ) 009(part1of3)0.0points 1. Which one of the following vectors is perpendicular to the line mx + ny = c . 1. n = n i m j 2. n = m i n j 3. n = n i + m j 4. n = 1 n i 1 m j 5. n = 1 m i + 1 n j 6. n = m i + n j 010(part2of3)0.0points 2. Use part 1 and scalar projection to find the distance from the point P ( a, b ) in the plane to the line mx + ny = c .

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test3review-problems - suleimenov(bs26835 test3review...

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