Let the plane $\pi : z = 1$, the points $\mathrm { P } ( 1,1,1 )$ and $\mathrm { Q } ( 0,0,1 )$ and the line $r$ passing through points P and Q.\ a) ( 0.25 points) Verify that points P and Q belong to the plane $\pi$.\ b) (1 point) Find a line parallel to $r$ contained in the plane $z = 0$.\ c) (1.25 points) Find a line passing through P such that its orthogonal projection onto the plane $\pi$ is the line $r$, and it forms an angle of $\frac { \pi } { 4 }$ radians with it.