Question

1.Describe the shape of the intersection of the plane z=-3 and the plane y=z in three space

2.List all the possibilities for the intersection of a line and a plane, and draw an example of each.

Answer 1

For 1: I got that y=z=-3
The shape of the intersection of the plane is a line for (x,3,3) for any x


For 2: I got the line can lie in the plane, The line can intersect the plane at a point, The line can be parallel to the plane, and the line doesn't intersect the plane at all. But how do I draw these??

Answer 2

not sure if these are right. anyone can verify and help?