Math Name: 20C. Midterm Exam 1 July 9, 2004
Student Number:
Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No credit will be given for illegible solutions.
1. (4 points) Consider the vectors v = 2i - 2j + k and w = i + 2j - k. (a) Compute v w.
(b) What is the cosine of the angle between v and w?
(c) Find a unit vector in the direction of v.
# 1 2 3 4
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2. (4 points) Find equation the of the plane that contains the lines r1 (t) = 1, 2, 3 t and r2 (t) = 1, 1, 0 + 1, 2, 3 t.
3. (4 points) Find an equation for the plane that passes through the points (2, 2, 0), (1, 0, 3), and (0, 1, 2).
4. (4 points) A particle moves along the curve r(t) = sin(3t), 4t, cos(3t) , for t 0. (a) F...