Prove this cross product and dot product = a scalar of itself

http://imgur.com/dF0TNPn.jpg

If i simply right this all down with a1b1c1 etc, will this be a valid proof? Or is there some quick way to prove it I am not seeing.

edit : I have proved it by writing it out the long way, but is there a quicker method?

Re: Prove this cross product and dot product = a scalar of itself

Quote:

Originally Posted by

**lukasaurus** http://imgur.com/dF0TNPn.jpg
If i simply right this all down with a1b1c1 etc, will this be a valid proof? Or is there some quick way to prove it I am not seeing.

edit : I have proved it by writing it out the long way, but is there a quicker method?

$\displaystyle a \cdot (b \times (mb + c)) = a \cdot (b \times (mb) + b \times c )$

$\displaystyle = a \cdot (m b \times b + b \times c)$

Can you finish?

-Dan