# 3D perpendicular distance

• March 18th 2010, 01:50 PM
jut
3D perpendicular distance
Given three points P1(-2, 0, 3), P2(0, 4, -1), and P3(3, 1, 3) find the perpendicular distance from point P3 to the line joining P1 and P2.

I have two tools; the dot and cross product. But I'm not seeing how to use them to obtain the $\perp$ distance.

For ease of notation let $\mathcal{A}=\overrightarrow {P_1 P_2 }~\&~\mathcal{B}=\overrightarrow {P_1 P_3 }$.
Then the distance you need is $\frac{||\mathcal{A}\times\mathcal{B}||}{||\mathcal {A}||}$