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

Answer

$(a) [0, 12]$
Explanation: Given that, $|\vec{a}|=4$ and $-3 \leq \lambda \leq 2$
We know that, $|\lambda \vec{a}|=|\lambda||\vec{a}|$
$\Rightarrow|\lambda \vec{a}|=|-3||\vec{a}|=3.4=12 \text { at } \lambda=-3$
$\Rightarrow|\lambda \vec{a}|=|0||\vec{a}|=0.4=0 \text { at } \lambda=0$
$\Rightarrow|\lambda \vec{a}|=|2||\vec{a}|=2.4=8 \text { at } \lambda=2$
Hence, the range of $|\lambda \vec{a}|$ is $(0,12)$.

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