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

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 $\gamma\cap \pi$ .