Question

Let $\vec{a}$ = 2$\widehat{i}$+3$\widehat{j}$+4$\widehat{k}$, $\vec{b}$ = $\widehat{i}$-2$\widehat{j}$-2$\widehat{k}$, $\vec{c}$ = -$\widehat{i}$+4$\widehat{j}$+3$\widehat{k}$ and $\vec{d}$ is a vector perpendicular to $\vec{b}$ and $\vec{c}$, $\vec{a}$.$\vec{d}$ = 18, then find |$\vec{a}$x$\vec{d}$|2

• A. 720
• B. 700
• C. 360
• D. 300

Answer 1

Answer: (A)

720

Answer 2

$\vec{d}=\lambda (\vec{b}\times \vec{c})=\lambda (2\widehat{i}-\widehat{j}+2\widehat{k})$
$\vec{a}.\vec{d}=18$
$\Rightarrow \lambda =2$
Therefore, $|\vec{a}\times \vec{d}|^{2}=\vec{a}^{2}\vec{d}^{2}-(\vec{a}.\vec{d})^{2}$
$\Rightarrow |\vec{a}\times \vec{d}|^{2}=29\times 36-324=1044-324=720$