If $|\mathbf{a}| = 4$ and $-3 \le \lambda \le 2$, then the range of $|\lambda \mathbf{a}|$ is

$[0, 12]$

The correct answer is Option (3) → $[0, 12]$ ##

We have, $|\mathbf{a}| = 4$ and $-3 \le \lambda \le 2$

$∴|\lambda \mathbf{a}| = |\lambda| |\mathbf{a}| = \lambda \cdot 4$

$\Rightarrow |\lambda \mathbf{a}| = |-3| \cdot 4 = 12, \text{ at } \lambda = -3$

$|\lambda \mathbf{a}| = |0| \cdot 4 = 0, \text{ at } \lambda = 0$

and $|\lambda \mathbf{a}| = |2| \cdot 4 = 8, \text{ at } \lambda = 2$

So, the range of $|\lambda \mathbf{a}|$ is $[0, 12]$.