Question

Find the scalar and vector products of two vectors, $a=(3\hat{i}-4\hat{j}+5\hat{k})$ and $b=(-2\hat{i}+\hat{j}-3\hat{k})$.

Answer 1

$a\cdot b=(3\hat{i}-4\hat{j}+5\hat{k})\cdot (-2\hat{i}+\hat{j}-3\hat{k})$
$=-6-4-15$
$=-25$
$a\times b=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& -4& 5\\ -2& 1& -3\end{array}\right|$ $=7\hat{i}-\hat{j}-5\hat{k}$
Note $b\times a=-7\hat{i}+\hat{j}+5\hat{k}$