If points A, B and C have position vectors 2 i, j and 2 k respectively, then show that ABC is an isosceles triangle.

$$\begin{aligned} & \overrightarrow{\mathbf{B A}}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}} ; \overrightarrow{\mathbf{B C}}=2 \hat{\mathbf{k}}-\hat{\mathbf{j}} \\ & |\overrightarrow{\mathbf{B A}}|=|\overrightarrow{\mathbf{B C}}|=\sqrt{5} \Rightarrow \Delta \mathbf{A B C} \text { is an isosceles triangle } \end{aligned} $$