Question

If \[\left| \overrightarrow{a} \right| = 4\] and \[- 3 \leq \lambda \leq 2\], then write the range of \[\left| \lambda \vec{a} \right|\].

Answer 1

We have `|vec∝| = 4 and -3 <= lambda <= 2`

∴ `|lambda veca| = |- 3| 4 = 12, at  lambda = - 3`

`|lambda veca| = |0| 4 = 0, at  lambda = 0`

And `|lambda vec∝| |2| 4 = 8, at  lambda = 2`

So, the range of `|lambda vec∝| is [0, 12].`

Alternate Method

Since, `- 3 <= lambda <= 2`

`0 <= || lambda| <= 3`

`= 0 <= 4| lambda| <= 12`

`|lambda veca| ∈ [0, 12]`