$\lvert \vec{a} \rvert = 3$ and $-4 \le \lambda \le 2$. What is the range of $\lvert \lambda\vec{a} \rvert$?

Explanation

1. 01

   $\lvert \lambda\vec{a} \rvert = 3\lvert \lambda \rvert$, and on $[-4, 2]$, $\lvert \lambda \rvert$ takes every value from $0$ (at $\lambda = 0$) to $4$ (at $\lambda = -4$).

2. 02

   So $\lvert \lambda\vec{a} \rvert$ runs over $[0, 12]$.