Lines and Planes in 3D

Theorem: Line and Point $⟹$ Plane

If $l$ is a straight lines and $P$ is a point which does not lie on $l$, then there exists a unique plane $\lambda$ which contains both $l$ and $P$.

PROOF

TODO

The Theorem of Three Perpendiculars

Let $a$ be a straight line which intersects the plane $\alpha$ and let $b$ be a straight line which lies in $\alpha$.

Then $a$ and $b$ are perpendicular if and only if the projection of $a$ onto $\alpha$ is perpendicular to $b$.

PROOF

TODO