Lines and Planes in 3D#

Theorem: Line and Point \(\implies\) Plane

If \(l\) is a [[Straight Lines in 3D|straight lines]] and \(P\) is a [[Euclidean Geometry|point]] which does not lie on \(l\), then there exists a unique [[Planes in 3D|plane]] \(\lambda\) which contains both \(l\) and \(P\).

![[res/Point and Line Imply Plane.svg]]

The Theorem of Three Perpendiculars

Let \(a\) be a [[Straight Lines in 3D|straight line]] which intersects the [[Planes|plane]] \(\alpha\) and let \(b\) be a [[Straight Lines in 3D|straight line]] which lies in \(\alpha\).

Then \(a\) and \(b\) are [[Straight Lines in 3D|perpendicular]] if and only if the [[TODO|projection]] of \(a\) onto \(\alpha\) is [[Straight Lines in 3D|perpendicular]] to \(b\).