If $|\vec{a}|=5, |\vec{b}|=2$ and $|\vec{a}.\vec{b}|=8$ then the value of $|\vec{a}×\vec{b}|$ is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6
$|\vec{a}.\vec{b}|=8$
$=|\vec{a}||\vec{b}|\cos θ=8$
$\cos θ=\frac{4}{5}$
$⇒\sin θ=\frac{3}{5}$
so $|\vec{a}×\vec{b}|=|\vec{a}||\vec{b}|\sin θ=5×2×\frac{3}{5}=6$