12.3-5soln

12.3-5soln - MATH 231 Group Work Quiz Related 1. Find a b ,...

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Unformatted text preview: MATH 231 Group Work Quiz Related 1. Find a b , a b , proj a b , and comp a b . Can you draw any conclusions about a and b from these results? (a) a = h 2 , 4 ,- 8 i and b = h 3 , 6 ,- 12 i . (b) a = h 1 , 2 , 4 i and b = h- 2 , 3 ,- 1 i . (c) a = h cos t,- sin t, 3 i and b = h- cos t, sin t, 1 i . Answer: (a) a b = 126, a b = ~ 0, proj a b = h 3 , 6 ,- 12 i , and comp a b = 3 21. The vectors are parallel. (b) a b = 0, a b = h- 14 ,- 7 ,- 7 i , proj a b = ~ 0, and comp a b = 0. The vectors are perpendicular. (c) a b = 2, a b = h- 4sin t,- 4cos t, i , proj a b = 1 5 h cos t,- sin t, 3 i , and comp a b = 2 10 . 2. Find the angle between a diagonal of a cube and a diagonal of one of its faces. Answer: For the sake of simplicity, let the cube be of length 1 and with sides parallel to the axes. Then the diagonal of one of the faces is h 1 , 1 , i and the diagonal of the cube is h 1 , 1 , 1 i . Thus, the angle between them is cos- 1 q 2 3 . 615 radians or 35...
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12.3-5soln - MATH 231 Group Work Quiz Related 1. Find a b ,...

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