If $(\vec{a}-\vec{b}) \cdot(\vec{a}+\vec{b})=27$ and $|\vec{a}|=2|\vec{b}|$, then $|\vec{b}|$ is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3
$(\vec{a}-\vec{b}) \cdot(\vec{a}+\vec{b})=27$
so $|\vec a|^2-|\vec b|^2=27$
$=4|\vec b|^2-|\vec b|^2=27$ (∵ $|\vec a|=2|\vec b|$)
$3|\vec b|^2=27$
$|\vec b|=3$