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Quiz #1
NAME:
#1(3 pts) Let u  (3,0,1) and v  (2, 2,1) .
a. Calculate projv (u ) .
b. Find a vector of length 3 that has the same direction as v .
#2(3 pts) Find the parametric equations and the symmetric equations of the line through (1, 4, 2)
x  6 y  3 1 z


that is parallel to the line with symmetric equations
.
3
2
2
#3(4 pts) Determine if the line given by the parametric formulas (2, 2,3)  t (1,0, 2) and the line
x  6 y  3 z 1


with symmetric equations
intersect. If so, at what point do they intersect?
4
2
4
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Challenge:
#4(3 pts) 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  .
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