\begin{aligned} &\text { 3.2 Given vectors } \mathbf{A}=\hat{\mathbf{x}} 2-\hat{\mathbf{y}} 3+\hat{\mathbf{z}}, \quad \mathbf{B}=\hat{\mathbf{x}} 2-\hat{\mathbf{y}}+\hat{\mathbf{z}} 3, \text { and }\\ &\mathrm{C}=\hat{\mathbf{x}} 4+\hat{\mathbf{y}} 2-\hat{\mathbf{z}} 2, \text { show that } \mathbf{C} \text {

is perpendicular to both } \mathrm{A}\\ &\text { and } \mathbf{B} \text { . } \end{aligned}