**Unformatted text preview: **=
v
ï¿¿4, 2, 0ï¿¿.
Answer:
The best answer is Dv f = ï¿¿4, âˆ’5ï¿¿ Â· âˆšï¿¿4,2ï¿¿ 16+4) âˆš
= 6/ 20 where we have replaced ï¿¿ 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: Ë†
i A normal vector to the plane is given by N = det 2
0
its angle with the vertical we have cos(Î¸) = ï¿¿0, 0, 1ï¿¿
âˆš
cosâˆ’1 (4/ 21) Ë†k
jË† Ë†
i
j
1 0 = Ë† âˆ’ 2Ë† + 4k . To calculate
21
âˆš
Â· N/ï¿...

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