Math 241 - Quiz #3

1. Find the parametric equations for the line through the points (3,1,-1) and (3,2,-6).

2. Find the equation of the plane through the point (6,5,-2) and parallel to the plane x + y - z + 1 = 0.

3. Change from cylindrical to rectangular (cartesian) coordinates: (1,pi,e).

Solutions:

x = 3
y = 1 + t
z = -1 - 5t

2. The normal for the plane is <1,1,-1>, so the general plane of this form is x + y - z = d. Plugging in (6,5,-2), we get d = 6 + 5 - (-2) = 13. Thus the equation is

x + y - z = 13

3. r = 1, theta = pi, z = e, so x = r cos theta = 1 cos pi = -1, y = r sin theta = 1 sin pi = 0, and z = e. Thus in rectangular coordinates the point is (-1,0,e).