MVC
SHOW ALL WORK !!
Calculator Allowed
Quiz #1
Name:
#1(5 pts) Find the parametric equations of the line through (1,0,2) that is parallel to the line given
 x  1  4t

by:  y  3  2t .
 z  2  t

#2(6 pts) Find the equation of the plane which is perpendicular to the line with equations
 x  1  4t

 y  3  2t and contains the point (1, 2,1) .
 z  2  t

MVC
( x  2) ( y  1) ( z  3)


intersect the plane given by
2
2
4
3x  5 y  z  2 . Explain/show work.
#3(6 pts) Does the line given by
#4(6 pts) Do the three planes given by 4 x  2 y  z  3 , 3 x  y  0 , and 3x  10 y  2 z  6 intersect
in a single line? If so, find the equation of the line. If not, clearly explain how you know.
MVC
#5(10 pt’s) Let u , v  3 . Determine whether each statement is true or false. If true, prove it. If
false, give an example that demonstrates it is false.
i.
ii.
MVC
u  v 
2
 u v
2
u v  u v
 u
2
v
2
 xt
 x  t 1


#6(6 pt’s) Find the distance between the lines given by  y  t  2 and  y  t .
 z  3t  1
 z  2t  1


MVC