Shortest Distance from a point to a plane

$${\text{proj}}_{\vec{n}}(\overrightarrow{PR})$$

• The idea is very similar to finding that for the line with a few differences.
• To do projections, we need a receiving vector, we used $\vec{d}$ in lines, here we’ll use $\vec{n}$.
• In lines we have a direction vector representing the direction of the line.
• In planes we have a normal vector perpendicular to the plane.
• Since $\vec{n}$ is perpendicular to the plane, the projection of $\vec{P}R$ onto $\vec{n}$ will give us the shortest distance itself.
• The perp will give us the distance from $P$ to $Q$ (the shortest distance-walla point).
• This is opposite to that of the plane where the perp gives the distance and proj gives the point.