Question

Fill in the blanks:

The distance from a point P to a line $ℒ$ parametrized by$\mathbf{r}\left(t\right)={\mathbf{P}}_{\mathbf{0}}+t\mathbf{d}$is ________ .

Short answer

The required expression is$\frac{||\mathbf{d}\times \underset{{\mathbf{P}}_0\mathbf{P}}{\to }||}{||\mathbf{d}||}$

Step-by-step solution

Given information

Given a point P and Line parameterized by$\mathbf{r}\left(t\right)={\mathbf{P}}_{\mathbf{0}}+t\mathbf{d}$

Filling in the blanks

The required distance is given by the expression:

$\frac{||\mathbf{d}\times \underset{{\mathbf{P}}_0\mathbf{P}}{\to }||}{||\mathbf{d}||}$