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Quiz #1
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#1(3 pt's) Find the parametric equations of the line that contains the point (1,2,3) and is parallel to
x  2 z+1

, y  4.
the line with symmetric equations
5
3
#2(4 pt’s). Let x = (3, 4, –1) and y = (–5, 2, 1).
a.
Find x .
b.
Find projx y
 x  1  2sin t

#3(4 pts) Describe the curve given parametrically by  y  3  sin t , 0  t  2 . (You need not
 z  2  3sin t

graph the curve). Be as explicit as possible. Describe the shape of the curve and how it is
traced out as t goes from 0 to 2 .
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#4(4 pt’s) Let u , v , w  3 . Determine whether each statement is true or false. If true, prove it. If
false, give an example that demonstrates it is false.
i.
If u  0 and u w  u v , then w  v
ii.
u v  u v
#5(5 pt's) Let x  (5, a,3a ) and y  (10, 4, 6a )
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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#6 (3 pt’s) Prove that the midpoints of a quadrilateral in
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3
form a parallelogram.