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Question
If `|vec"a"|` = 4 and −3 ≤ λ ≤ 2, then the range of `|lambdavec"a"|` is ______.
Options
[0, 8]
[–12, 8]
[0, 12]
[8, 12]
Solution
If `|vec"a"|` = 4 and −3 ≤ λ ≤ 2, then the range of `|lambdavec"a"|` is [–12, 8].
Explanation:
Given that `|vec"a"|` = 4, −3 ≤ λ ≤ 2
Now `|lambdavec"a"| = lambda|vec"a"| = lambda * 4 = 4lambda`
Here −3 ≤ λ ≤ 2
⇒ `-3.4 ≤ 4lambda ≤ 2.4`
⇒ `-12 ≤ 4lambda ≤ 8`
∴ `4lambda` = [–12, 8]
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