Vector Algebra — Class 12 Maths Solution

Here, $|\overrightarrow {\rm{a}} | = 10,|\overrightarrow {\rm{b}} | = 2$

and $\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} = 12\quad$

[given]
$\therefore \overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} = |\overrightarrow {\rm{a}} ||\overrightarrow {\rm{b}} |\cos \theta$

$12 = 10 \times 2\cos \theta$
$\Rightarrow$ $\cos \theta = \frac{{12}}{{20}} = \frac{3}{5}$

$\Rightarrow$ $\sin \theta = \sqrt {1 - {{\cos }^2}\theta } = \sqrt {1 - \frac{9}{{25}}}$

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

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