# Vector Calculas: Simplifying expressions

gotpho

## Homework Statement

(a -b) $$\cdot$$ (b - c) $$\times$$ (c - a)

## The Attempt at a Solution

Honestly I have no idea where to being. I believe this expression is a scalar triple product but I do not know how to use the properties to simplify this expression.

Sorry, kind of screw up the latex symbols. Not sure how to use it probably.

Mentor
As you've written it, the expression doesn't make any sense. If you calculate (a - b) $\cdot$ (b - c), you get a scalar, which you can't cross with a vector. Do you mean
(a - b) $\cdot$ ((b - c) X (c - a))?

If so, here's a Wikipedia article that might be of help to you - http://en.wikipedia.org/wiki/Scalar_triple_product#Scalar_triple_product

gotpho
As you've written it, the expression doesn't make any sense. If you calculate (a - b) $\cdot$ (b - c), you get a scalar, which you can't cross with a vector. Do you mean
(a - b) $\cdot$ ((b - c) X (c - a))?

If so, here's a Wikipedia article that might be of help to you - http://en.wikipedia.org/wiki/Scalar_triple_product#Scalar_triple_product

Perhaps but the book wrote it as (a - b) $\cdot$ (b - c) X (c - a). The book says the answers is 0 but I'm clueless as to where to begin. I'm guessing we have to simplify the cross product first.