Vector Algebra

Given, \(\mathbf{a}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) and \(\mathbf{b}=\mathbf{b}_1+\mathbf{b}_2\) where \(\mathbf{b}_1\) is parallel to \(\mathbf{a}\) and \(\mathbf{b}_2\) is perpendicular to \(\mathbf{a}\). Then, \(\mathbf{b}_2\) is equal to