--------- 50 points --------
Prove that :-
![\hat{i} \times \hat{i} = 0 \\ \ \textless \ br /\ \textgreater \ \hat{i} \times \hat{j} = \hat{k} \\ \ \textless \ br /\ \textgreater \ \hat{j} \times \hat{i} = - \hat{k} \hat{i} \times \hat{i} = 0 \\ \ \textless \ br /\ \textgreater \ \hat{i} \times \hat{j} = \hat{k} \\ \ \textless \ br /\ \textgreater \ \hat{j} \times \hat{i} = - \hat{k}](https://tex.z-dn.net/?f=+%5Chat%7Bi%7D++%5Ctimes+%5Chat%7Bi%7D+%3D+0+%5C%5C+%5C++%5Ctextless+%5C+br+%2F%5C++%5Ctextgreater+%5C+%5Chat%7Bi%7D+%5Ctimes+%5Chat%7Bj%7D+%3D+%5Chat%7Bk%7D+%5C%5C++%5C++%5Ctextless+%5C+br+%2F%5C++%5Ctextgreater+%5C+%5Chat%7Bj%7D+%5Ctimes+%5Chat%7Bi%7D+%3D++-+%5Chat%7Bk%7D)
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