Question

If `|vec"a"|` = 3 and –1 ≤ k ≤ 2, then `|"k"vec"a"|` lies in the interval ______.

Options

• [0, 6]

• [– 3, 6]

• [3, 6]

• [1, 2]

Answer 1

If `|vec"a"|` = 3 and –1 ≤ k ≤ 2, then `|"k"vec"a"|` lies in the interval [0, 6].

Explanation:

The smallest value of `|"k"vec"a"|` will exist at numerically smallest value of k

i.e., at k = 0

Which gives `|"k"vec"a"| = |"k"||vec"a"|`

= 0 × 3

= 0

The numerically greatest value of k is 2 at which `|"k"vec"a"|` = 6.