Question

If $a=i-j$ and $b=j+k,$ then $|a\times b{|}^2+|a\cdot b{|}^2$ is equal to :

• A. $\sqrt{2}$
• B. $2$
• C. $\sqrt{6}$
• D. $4$
• E. $6$

Answer 1

The correct option is D $4$

Given, $a=i-j$ and $b=j+k$
Thus $a\times b=\left|\begin{array}{ccc}i& j& k\\ 1& -1& 0\\ 0& 1& 1\end{array}\right|$
$=i(-1-0)-j(1-0)+k(1-0)$
$=-1-j+k$
and $a\cdot b-(i-j)\cdot \left(j_k\right)=-1$
Therefore, $|a\times b{|}^2+|a\cdot b{|}^2=[\sqrt{\left)\right(-1{)}^2+(-1{)}^2+(1{)}^2}{]}^2+(-1{)}^2$
$=(\sqrt{3}{)}^2+1$
$=3+1=4$