Question

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=\sqrt{14},|\vec{b}|=\sqrt{6}$ and $|\vec{a} \times \vec{b}|=\sqrt{48}$ Then $(\vec{a} \cdot \vec{b})^2$ is equal to

Answer 1

The correct answer is 36.
∣a∣=14​,∣b∣=6​∣a×b∣=48​
∣a×b∣2+∣a⋅b∣2=∣a∣2×∣b∣2
⇒(a⋅b)2=84−48=36