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]

Answer 1

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]