Vector Algebra — Class 12 Maths Solution

We have, $|\vec a| = 4$ and $- 3 \le \lambda \le 2$

$\therefore$
$\Rightarrow$ $|\lambda \overrightarrow {\rm{a}} | = | - 3|4 = 12$, at $\lambda = - 3$

$|\lambda \vec a| = |0|4 = 0$, at $\lambda = 0$

and $|\lambda \overrightarrow {\rm{a}} | = |2|4 = 8$, at $\lambda = 2$

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

Alternate Method
Since, $- 3 \le \lambda \le 2$
$0 \le |\lambda | \le 3$

$\Rightarrow$ $0 \le 4|\lambda | \le 12$
$|\lambda \overrightarrow {\rm{a}} | \in [0,12]$