Given the parametric equation of a line, and the equation of a plane, how can you find the "orthogonal projection of the line onto the plane"?

Help very very appreciated!! Thanks!

- Jun 3rd 2011, 02:45 AMYehiaIn 3D space, how do you find the "orthogonal projection of a line onto a plane"?
Given the parametric equation of a line, and the equation of a plane, how can you find the "orthogonal projection of the line onto the plane"?

Help very very appreciated!! Thanks! - Jun 3rd 2011, 06:50 AMFernandoRevilla
One way: express the line $\displaystyle L$ as intersection of two planes $\displaystyle (\pi_1=0)\wedge (\pi_2=0)$. The equation of all planes containing $\displaystyle L$ is $\displaystyle \alpha \pi_1+\beta \pi_2=0$ with $\displaystyle \alpha,\beta\in\mathbb{R}$ . Choose among them the plane $\displaystyle \gamma$ orthogonal to the given plane $\displaystyle \pi$ . The solution is $\displaystyle \gamma\cap \pi$ .