Vector Calculas: Simplifying expressions

[gotpho]

Homework Statement

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

Homework Equations

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.

 

[Mark44]

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.