Mathematica 2 questions related to mathematical vectors

[AmrAmin]

I hope I can find a solutions for those questions with your help.

1. If you know that: A=(5,-4,3) B=(2,3,-1) C=(-3,2,5) .Find the volume of the prism whose sides are \underline{OA}, \underline{OB}, \underline{OC} .

2. Prove using vector components that:

\underline{a} \times \left(\underline{b} \times \underline{c}) = (\underline{a} . \underline{c})\underline{b} - (\underline{a} . \underline{b})\underline{c}
and using this rule prove that :

\underline{a} \times (\underline{b} \times \underline{c}) + \underline{b} \times (\underline{c} \times \underline{a}) + \underline{c} \times (\underline{a} x \underline{b}) = 0

 

[chaoseverlasting]

Well? You want to give us some ideas about where you're stuck? We're not going to do it for you. We're here to help you along.