Question

If ${\left|\vec{a}+\vec{b}\right|^2}$ + ${\left|\vec{a} \cdot \vec{b}\right|^2} =144$ $|\vec{a}| =6$ then $|\vec{b}|$ is equal to

• A. 6
• B. 3
• C. 2
• D. 4

Answer 1

Answer: (C)

$|\vec{a} \times \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=144$
$\Rightarrow |\vec{a}|^{2}|\vec{b}|^{2} \sin ^{2} \theta+|\vec{a}|^{2}|\vec{b}|^{2} \cos ^{2} \theta=144$
$\Rightarrow |\vec{a}|^{2}|\vec{b}|^{2}=144$
$\Rightarrow |\vec{b}|^{2}=\frac{144}{36}=4 \,\,\,(\because|\vec{a}|=6)$
$\Rightarrow |\vec{b}|=2$