In 3D space, how do you find the "orthogonal projection of a line onto a plane"?

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June 3rd 2011, 02:45 AM
Yehia

In 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!
June 3rd 2011, 06:50 AM
FernandoRevilla

One way: express the line $L$ as intersection of two planes $(\pi_1=0)\wedge (\pi_2=0)$ . The equation of all planes containing $L$ is $\alpha \pi_1+\beta \pi_2=0$ with $\alpha,\beta\in\mathbb{R}$ . Choose among them the plane $\gamma$ orthogonal to the given plane $\pi$ . The solution is $\gamma\cap \pi$ .

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