I wish to know if there are other properties of the vector product that I should know apart from the standard ones : distributive over addition multiplication by a constant and $a\times b=-b\times a$ The fact is I am stuck on this proof since 3 hours please help
Show that for three points A,B,C (non collinear) of space and For any point M ,
$\vec{MA}\times \vec{MB}+\vec{MB}\times \vec{MC}+\vec{MC}\times \vec{MA} = \vec{AB}\times \vec{AC}$
I think the key to answering this question is knowing that $\vec{XY}=\vec{ZY}-\vec{ZX}$.
If you let $M$ be the origin the equation you need to prove becomes:
$$\vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a} = (\vec{b}-\vec{a})\times (\vec{c}-\vec{a})$$
You also need to know that $\vec x\times\vec x=\vec0$.