Hello, Jenny!

There are a number of approaches . . . here's one.

The graph of the equation is a plane

passing through the origin with normal vector

The answer is True . . . why?

Converting from Cylindrical to Rectangular, we have: .

If you sketch (or visualize) this plane, its trace is the 45° line on the "left wall".

. . The plane extends infinitely to the left and right.

So itdoespass through the origin.

Now we must find its normal vector.

Pick three points on the plane:

We have two vectors in the plane: .

The normal vector of the plane is perpendicular to both and .

Hence: .

Therefore: . . . . The statement istrue.