As the title says, I have to find a plane parallel to the z-axis and the line $r = (\lambda + 1, \lambda - 1, 1 - \lambda)$. The plane also passes through the point $A(-2, 3, 0)$.
Now, I was thinking, since the plane is parallel to the $z$-axis, then the normal vector of the plane would be perpendicular to the $z$-axis. Am I wrong here?
Could someone solve this task step-by-step, explaining the reasoning as best as possible? I can't seem to figure it out...
Thanks in advance!