Let the line $r \equiv \left\{ \begin{array} { l } x = \lambda \\ y = 0 \\ z = 0 \end{array} \right.$ and the plane $\pi : z = 0$.
a) (1 point) Find an equation of the line parallel to the plane $\pi$ whose direction is perpendicular to $r$ and passes through the point $( 1,1,1 )$.
b) (1.5 points) Find an equation of a line that forms an angle of $\frac { \pi } { 4 }$ radians with the line $r$, is contained in the plane $\pi$ and passes through the point ( $0,0,0$ ).