MTH164FA10-M1d_ans

By what angle does the tower now deviate from the

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Unformatted text preview: = v ￿4, 2, 0￿. Answer: The best answer is Dv f = ￿4, −5￿ · √￿4,2￿ 16+4) √ = 6/ 20 where we have replaced ￿ by the v parallel unit vector. Answer: 2. (5 points) A million years ago, an alien species built a vertical tower on a horizontal plane. When they returned, they discovered that the ground had tilted so that the measurements of 3 points on the ground gave coordinates of P (0, 0, 0), Q(2, 1, 0) and R(0, 2, 1). By what angle does the tower now deviate from the vertical? (Leave answer in terms of arccosine.) Answer: ˆ i A normal vector to the plane is given by N = det 2 0 its angle with the vertical we have cos(θ) = ￿0, 0, 1￿ √ cos−1 (4/ 21) ˆk jˆ ˆ i j 1 0 = ˆ − 2ˆ + 4k . To calculate 21 √ · N/...
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This document was uploaded on 05/06/2013.

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