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SHOW ALL WORK !!
Sample Quiz #1
#1(5 pt's) Find the equation of the plane through (1,0,2) that is parallel to the xy-plane.
Solution: z = 2
Any plane parallel to the xy-plane has equation z = constant.
#2(5 pt's) Find the parametric equations of the line of intersection of the two planes given by:
2x – 3y + 4z = 2 and x + 4z = – 2
( x  2) ( y  1) ( z  3)
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intersect the plane given by
2
2
4
3x  5 y  z  2 . Explain/show work.
#3(4 pts) Does the line given by
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 x  2t  1
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#4(4 pt's) Find the angle between the line given by  y  t  1 and the plane given by
 z  t 3
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4x  2 y  z  0
#5(8 pt’s) Let u , v , w R 3 and a  R . Determine whether each statement is true or false. If true,
prove it. If false, give an example that demonstrates it is false.
a. a(u  v )  au  av
b.
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If u  (v  w)  0, then u , v , and w all lie in the same plane.
 x  2t  3
 x  3t  1
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#6(4 pt’s) Find the distance between the lines given by  y  t  1 and  y  2t .
 z  3t  2
 z  t  2
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