Animação do esboço de reta perpendicular a duas retas reversas

A reta $$r_3\,:\; \left\{\begin{array}{lll} x&=&1\\ y&=&2,\\ z&=&3t\end{array}\right.\,\mbox{para todo $t\in\mathbb{R}$.} $$ intercepta as retas $$r_1\,:\; \left\{\begin{array}{lll} x&=&-1+2t\\ y&=&1+t,\\ z&=&0\end{array}\right.\,\mbox{para todo $t\in\mathbb{R}$} $$ e $$r_2:\; x-2=\frac{y-4}{2}\;\quad\mbox{e}\quad z=3$$ e é perpendicular a ambas.