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# Ch09

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### Ch09

1. 1. Chapter 9 Test Bank 117 Test Form A Name __________________________________________ Date ____________________________ Chapter 9 Class __________________________________________ Section _______________________ 1. Find a unit vector in the direction of v if v is the vector from P 1, 2, 3 to Q 4, 1, 0 . 1 1 1 (a) 3i 3j 3k (b) i j k (c) i j k 3 3 3 1 1 1 (d) i j k (e) None of these 3 3 3 2. Calculate j i. (a) j (b) k (c) k (d) i (e) None of these In problems 3 through 8, let u 3i j 2k, v 2i 3j 2k and w i 2k. 3. Calculate u v. (a) 7 (b) 13 (c) 8, 2, 11 (d) 1 (e) None of these 4. Calculate u v. (a) 4, 10, 11 (b) 8, 2, 11 (c) 7 (d) 4, 10, 11 (e) None of these 5. Calculate u v w. (a) 30 (b) 18i 6j 6k (c) 16 (d) 24 (e) None of these © Houghton Mifflin Company. All rights reserved. 6. Calculate projvu. 7 14 21 14 (a) 17 (b) 17 , 17 , 17 (c) 17 (d) 14, 21, 14 (e) None of these 7. Calculate cos where is the angle between u and v. 7 7 13 13 (a) (b) (c) (d) (e) None of these 2 17 238 238 2 17 8. Which of the following vectors is orthogonal to both u and v? (a) k (b) 8i 2j 11k (c) v u (d) w (e) None of these
2. 2. 118 Chapter 9 Vectors and the Geometry of Space 9. Which of the following is an orthogonal pair of vectors? (a) 2i j, i k (b) i j 2k, i j k (c) 3i 2k, 2j k (d) 5i j k, i 2j 3k (e) None of these 10. Which of the following is a set of parametric equations for the line through the points 2, 0, 3 and 4, 3, 3 ? (a) x 2 2t (b) x 2 2t (c) x 2 2t y t y 3t y t z 3 t z 3 z 3 (d) x 2 4t (e) None of these y 3t z 3 3t x y 1 z 1 11. Write an equation of the plane that contains the line given by and is 1 3 2 x 1 y 5 z 3 perpendicular to the line given by . 17 1 7 (a) 17x y 7z 6 0 (b) x 3y 2z 8 0 (c) x 3y 2z 1 0 (d) 17x y 7z 1 0 (e) None of these 12. Which of the following is a sketch of the plane given by 2x y 3z 6? (a) z (b) z 6 3 4 1 1 2 1 4 2 3 2 6 x 3 y x 6 y (c) z (d) z 6 6 4 4 © Houghton Mifflin Company. All rights reserved. 2 4 2 4 6 4 6 x y x 6 y (e) None of these 13. Calculate the distance from the point 1, 2, 3 to the line given by x 2 t, y 1, and z 1 t. 5 3 5 (a) (b) (c) 2 14 14 3 (d) (e) None of these 2