Q 18. - Calculus

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.

Step-by-Step Solution

Answer

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

Step 1: Given information

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

Step 2: Calculation

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

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