If $\vec a$ and $\vec b$ are two vectors such that $|\vec a| = 10, |\vec b| = 2$ and $\vec a.\vec b = 12$, then $|\vec a ×\vec b|$ is equal to

16

The correct answer is Option (1) → 16

$| \vec{a} | = 10,\; | \vec{b} | = 2,\; \vec{a}\cdot\vec{b} = 12$

$\vec{a}\cdot\vec{b} = |\vec{a}||\vec{b}|\cos\theta \Rightarrow 12 = (10)(2)\cos\theta$

$\Rightarrow \cos\theta = \frac{12}{20} = \frac{3}{5}$

$|\vec{a}\times\vec{b}| = |\vec{a}||\vec{b}|\sin\theta$

$\sin\theta = \sqrt{1-\cos^{2}\theta} = \sqrt{1 - \left(\frac{3}{5}\right)^{2}} = \frac{4}{5}$

$|\vec{a}\times\vec{b}| = (10)(2)\left(\frac{4}{5}\right) = 16$