Chapter 3, Problem 1CTB

In ${ℝ}^3$ , let ${\text{x}}_1$ and ${\text{x}}_2$ be linearly independent vectors and let ${\text{x}}_3=0$ (the zero vector). Are ${\text{x}}_1{\text{,x}}_2$ and ${\text{x}}_3$ linearly independent? Prove your answer.