Vector Algebra

The sides of a parallelogram are represented by vectors \(\vec{p}=5 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\vec{q}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\). Then, the area of the parallelogram is