Question

Explain the similarities in the derivations of the formulas for the distances from a point to a plane and from a point to a line.

Short answer

$\frac{||\mathbf{d}\times \overrightarrow{P_{0}P}||}{\Vert \mathbf{d}\Vert }$

Step-by-step solution

Given information

The line $\mathbf{r}\left(t\right)$and the point $P_0$on the line and the given point $P$

Calculation

The distance from point $P$ to the line $\mathbf{r}\left(t\right)$ is given by:

Distance $=\frac{||\mathbf{d}\times \overrightarrow{P_{0}P}||}{\Vert \mathbf{d}\Vert }$