Projection of a line onto a plane

The orthogonal projection of a line onto a plane is a fundamental problem in solid geometry. To find the line $\Delta$ – the projection of $d$ onto $(P)$, construct the plane $(\alpha)$ containing $d$ and perpendicular to $(P)$, then take the intersection $\Delta = (\alpha) \cap (P)$. The method employs direction and normal vectors to accurately derive the parametric equations of $\Delta$. Through a specific example with given $d$ and $(P)$, this article illustrates each step in detail, from establishing the equation of $(\alpha)$ to obtaining the parametric form of the projection....

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