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)

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