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