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Quiz #1
NAME:
#1(6 pts) Find the parametric equations of the line that contains the point (1,2,3) and is parallel to
x  2 z+1
the line with symmetric equations

, y  4.
5
3
#2(8 pts). Let x = (3, 4, –1) and y = (–5, 2, 1).
a.
Find a vector in the direction of x that is 3 units long.
b.
Find projx y
 x  1  2t
 x  5  2s


#3(8 pts) Do the lines given by  y  3  t and  y  2  s intersect? If so, find the point of
 z  2  3t
 z  5  s


intersection.
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#4(5 pt’s) Let u , v 
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3
. Prove that  u  v   u  v
2
2
 u
2
v
2
A longbow curve is defined as follows. Draw a circle in the xy-plane with radius a and center
(0, a) and draw the horizontal line y  2a . Each non-horizontal line through the origin intersects
the circle at a point A and the line y  2a at point B. Let P be the midpoint of the segment from A
to B. The set of all points P obtained in this way traces out the longbow curve as the lines through
the origin rotate from   0 to    , where  is the angle the line makes with the positive x axis.
Find a parametrization of this curve in terms of the angle  .
B
P
A
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