Question

Given $\overline{a}=x\hat{i}+y\hat{j}+2\hat{k},\overline{b}=\hat{i}-\hat{j}+\hat{k},\overline{c}=\hat{i}+2\hat{j}$; Angle $(\overline{a}$ and $\overline{b})=\pi /2,\overline{a}.\overline{c}=4$ then

• A. $[\overline{a}\overline{b}\overline{c}{]}^2=\left|\overline{a}\right|$
• B. $\left[\overline{a}\overline{b}\overline{c}\right]=\left|\overline{a}\right|$4
• C. $\left[\overline{a}\overline{b}\overline{c}\right]=0$
• D. $\left[\overline{a}\overline{b}\overline{c}\right]={\left|\overline{a}\right|}^2$

Answer 1

The correct option is D $\left[\overline{a}\overline{b}\overline{c}\right]={\left|\overline{a}\right|}^2$

$\overrightarrow{a}\cdot \overrightarrow{b}=0orx-y+2=0\&\overrightarrow{a}\cdot \overrightarrow{c}=4orx+2y=4$ so, $x=0\&y=2$
$\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]=\left|\begin{array}{ccc}0& 2& 2\\ 1& -1& 1\\ 1& 2& 0\end{array}\right|=8={\left|\overrightarrow{a}\right|}^2$