MVC
Quiz #1
NAME:
Show all appropriate work and thinking to receive full credit.
Calculator allowed. Explain briefly how you are using your calculator.
#1(4 pt's) Find the parametric or symmetric equations of the line of intersection of the two planes
given by: 3x  2 y  z  2 and 2 x  y  2 z  2 .
#2(6 pt’s) a. Find the parametric and symmetric equations for the line in
point (1,2,1) and perpendicular to the plane given by 7 x  y  z  59 .
b. Find the point of intersection of this line with the plane.
3
through the
#3(4 pts) Given the vectors y  (1, c  2,5) and z  (c  1, 2,3c  7) .
Find all value(s) of c that will make y and z parallel.
#4(6 pt's) Find the distance between the two lines L1 and L2, where the parametric equations for line
 x  1  3t
 x  4  3t


L1 are:  y  3  2t ; and line L2 is given by:  y  4  2t .
 z  4t
 z  11  t


#5(6 pt’s) Let u , v , w  3 and a,b  . Determine whether each statement is true or false. If
true, prove it. If false, give an example that demonstrates it is false.
a. If u  0 and u w  u v , then w  v
b.
u v  u
v