If \(-3 \le k \le 1\) and \(|\vec{a}| = 2\) then \(|k\vec{a}|\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → [0, 6]
The magnitude of a scalar multiple is
\(|k\vec{a}| = |k|\,|\vec{a}| = 2|k|\)
For \(-3 \le k \le 1\), |k| is smallest at k = 0 and largest at k = −3:
\(0 \le |k| \le 3\)
\(0 \le 2|k| \le 6\)
So \(|k\vec{a}|\) lies in [0, 6]. A magnitude is never negative, so [−6, 2], the range of 2k, cannot be the answer.