Can a plane be perpendicular to the x-axis and contain the line x=z, y=0? Explain.?

Answer 1

No. A plane perpendicular to the x-axis would be of the form:

x = k
where k is a constant

Remember a plane is perpendicular to its normal vector. The normal vector to the plane x = k is the vector n = <1, 0, 0>. The vector n is parallel to the x-axis. Any non-zero multiple of n would be a normal vector to the plane as well.