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# practice 5 answers - PRACTICE5 Name Section 1 Determine the...

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PRACTICE5 Name Section 1. Determine the angle between the vectors: (you can use a calculator) (a) a 4 , 3 A and a− 4 , 2 A cos 1 p 1 5 P (b) a− 3 , 2 A and a− 8 , 12 A cos 1 p 0 13 208 P = 90 (c) a 5 , 4 A and a 1 , 9 A cos 1 p 41 41 82 P = 45 (d) a 2 , 1 , 8 A and a 1 , 3 , 2 A cos 1 p 15 69 14 P 2. Determine the unit vector in the direction of: (a) a 5 , 12 A vu = a 5 13 , 12 13 A (b) 3 v i + 5 v j + 8 v k = 3 98 v i + 5 98 v j + 8 98 v k 3. Determine the scalar and vector projection of v F onto v d if: v F = a 1 , 8 A and v d = a 12 , 5 A sp = 42 13 v Vp = 42 169 a 12 , 5 A 4. Determine the cross product of the vectors: (a) a 3 , 5 , 1 A and a− 2 , 3 , 4 A v i v j v k 3 5 1 2 3 4 = 17 v i 10 v j + 1 v k (b) a 0 , 5 , 8 A and a 4 , 0 , 2 A v i v j v k 0 5 8 4 0 2 = 10 v i + 32 v j 20 v k

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5. Determine the area of the parallelogram formed by the vectors va = a 5 , 2 A and v b = a− 1 , 7 A . v v v v v 5 2 1 7 v v v v v = 37 6. Determine the area of the parallelogram formed by the vectors = a 4 , 5 , 8 A and v b = a 1 , 4 , 5 A . v v v v v v v v i v j v k 4 5 8 1 4 5 v v v v v v v = | 57 v i 12 v j 21 v k | = 57 2 + 12 2 + 21 2 7. Determine the volume of the parallelopiped formed by the vectors = a 3 , 4 , 1 A , v b = a 5 , 2 , 4 A , and v c = a− 1 , 3 , 3 A . v v v v v v v 3 4 1 5 2 4 1 3 3 v v
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