MVC
Quiz #2
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) Write the parametric equations of the line that goes through the points (1,1,1) and
(3, 2, 1) .
#2(5 pt’s) Write
 xs

 y  2  s and
 z  1  3s

the equation of the plane containing that contains the two lines given by
 x  5  2t

 y  1 t
 z  4t

#3(6 pt's) Label each expression as a Vector (V), a Scalar (S), or as Meaningless (M).
[Dot,  , always refers to dot product.]
(a)
u  u  v 
(b)
u  v   w
(c)
 u v   v u 
(d)
 i  j w
(f)
 u  v   v   w  i
(e)
u v v
#4(5 pt's) Prove that for a , b 
3

 

, a  b  a  b  2a  b
#5(6 pt’s) Find the distance between the planes given by 4 x  6 y  2 z  2 and 2 x  3 y  z  7 .
#6(6 pts) Given the vectors y  (1, 2c  3,5) and z  (c  1, 2, 10) .
a. Find all value(s) of c that will make y and z orthogonal.
b. Find all value(s) of c that will make y and z parallel
Spherical/Cylindrical
 r   sin 

  
 z   cos 

  2  r2  z2

r

 tan  
z

   
Spherical/Cartesian
 x   sin  cos 

 y   sin  sin 
 z   cos 


2
2
2
2
  x y z

x2  y 2

tan



z

y

tan  

x
#7(5 pts) Convert the equation  cos( )   sin( )  csc( ) into an equivalent equation in
Cartesian coordinates and then sketch its graph. [If you want to clarify your picture you may
describe the graph in words]
#8(5 pts) Sketch the region described by the intersection of the sets {(  ,  , ) cos( )   sin 2 ( )}
and {(  ,  , ) 1  } . [If you want to clarify your picture you may describe the graph in words]
#9(3 pts) Suppose a circle of radius a rolls along the line y  x . Find the parametric equations for
the path of the point P on the circle, starting at the origin. Use the angle t through which the circle
has rotated as the parameter.
P
t
P