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Quiz #1
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#1.(3 pt’s) Let u  (3, 4,1) and v  (5, 2,1) . Calculate projv (u ) .
#2(3 pt's) Find the parametric equations of the line through (1, 4, 2) and (5, 4, 2) .
#3(4 pts) Determine if the lines given by the parametric formulas (2, 2, 3) + t(1, 0, -2) and
(6, 3, 1) + s(4, 2, 4) intersect. If so, at what point do they intersect?
#4(3 pt’s) Prove that for u , v 
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: u v  u v
#5(3 pt’s) Find three non-parallel non-zero vectors orthogonal to u  (3, 4,1).
#6(5 pt's) Let x  (2, a,1  a) and y  (6, 9, 6)
a. Find all values of a such that x and y orthogonal.
b. Find all values of a such that x and y parallel.
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