If $|\vec{a}|=8,|\vec{b}|=3,$ and $|\vec{a}×\vec{b}|=12,$ then the value of $\vec{a}.\vec{b}$ is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $12\sqrt{3}$
$|\vec a|=8,|\vec b|=3$
$|\vec a×\vec b|=|\vec a||\vec b|\sin θ=12$
$⇒8×3\sin θ=12$
$⇒\sin θ=\frac{1}{2}$
$⇒θ=\sin^{-1}\left(\frac{1}{2}\right)=30°$
$∴|\vec a.\vec b|=|\vec a||\vec b|\cos θ$
$=8×3×\cos 30°$
$=24×\frac{\sqrt{3}}{2}$
$=12\sqrt{3}$