Vector problem: distance between a point and a line

[Clara Chung]

Homework Statement

Homework Equations

The Attempt at a Solution

My answer is d = |(a-b)x(p-b)|/|(b-a|). I first find out the area of the parallelogram produced by BA and BP and divide the area by length AB to get the height. Why am I wrong?

 

[kuruman]

You have a triangle formed by $(\vec b - \vec a)$, $(\vec p - \vec a)$ and $(\vec p - \vec b)$. Write its area in two different ways and set them equal.

 

[Clara Chung]

You have a triangle formed by $(\vec b - \vec a)$, $(\vec p - \vec a)$ and $(\vec p - \vec b)$. Write its area in two different ways and set them equal.

I see. I can also use the side p-a and p-b. Thank you.