Question

If $|\vec{a}\times \vec{b}{|}^2+|\vec{a}\cdot \vec{b}{|}^2=144$ and $|\vec{a}|=4$, then $|\vec{b}|$ is equal to :

• A. 12
• B. 3
• C. 8
• D. 4

Answer 1

Answer: (B)

$|\vec{a}\times \vec{b}{|}^2+|\vec{b}\cdot \vec{b}{|}^2=|\vec{a}{|}^2|\vec{b}{|}^2$
Given $|\vec{a}\times \vec{b}{|}^2+|\vec{a}\cdot \vec{b}{|}^2=144$
and $|\vec{a}|=4$
$|\vec{a}\times \vec{b}{|}^2+|\vec{a}\cdot \vec{b}{|}^2=|\vec{a}{|}^2|\vec{b}{|}^2$
$\Rightarrow 144=16\cdot |\vec{b}{|}^2$
$\Rightarrow |\vec{b}{|}^2=9$
$\Rightarrow |\vec{b}|=3$