If $|a| = 10, |b| = 2$ and $a \cdot b = 12$, then the value of $|\vec{a} \times \vec{b}|$ is

16

The correct answer is Option (4) → 16 ##

Here, $|a| = 10, |b| = 2$ and $a \cdot b = 12$ [given]

$∴a \cdot b = |a||b| \cos \theta$

$12 = 10 \times 2 \cos \theta$

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

$∴\sin \theta = \sqrt{1 - \cos^2 \theta}$

$= \sqrt{1 - \frac{9}{25}}$

$\sin \theta = \pm \frac{4}{5}$

Now, $|a \times b| = |a||b| \sin \theta$

$= 10 \times 2 \times \frac{4}{5} = 16$