Vector Algebra

Let \(\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=\hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{c}=\hat{\mathbf{k}}-\hat{\mathbf{i}}\) if \(\mathbf{d}\) is a unit vector such \(\mathbf{a} \cdot \mathbf{b}=0=[\mathbf{b} \mathbf{c} \mathbf{d}]\), then \(\mathbf{d}\) is