Solving the Triple Scalar Product: Finding the Value of a(dot)(a(cross)b)

[CaityAnn]

Homework Statement

What is the value of a(dot)(a(cross)b) ? Why?
I am supposed to find an actual value.
Sorry I don't know code, these variables are all vectors. A is dotted with vectors a and b which are cross product.

Homework Equations

I know this can be written as a determinate of all three variables but I do not see how this gives me a single answer.

The Attempt at a Solution

 

[AKG]

axb is perpendicular to a and b. The relevant part of this is that it is perpendicular to a, so axb is some vector c perpendicular to a. So what is a.c when c is perpendicular to a?

 

[^_^physicist]

Try this, write out the cross product by hand.

Once you have the cross product, take the scalar product.

(There is a trick to this question, see if you can find it).

 

[HallsofIvy]

^ ^physicist, you're evil! Yes, once CaityAnn has gone through that pain, perhaps she will learn that it is better to think!

 

[^_^physicist]

It may be evil, but I find if you work through it this way, after doing it a couple of times you start seeing the trick...