Exercise 37

Use the scalar triple product to verify that the vectors \(\mathbf{u} = \mathbf{i} + 5\mathbf{j} - 2\mathbf{k}, \mathbf{v} = 3\mathbf{i} - \mathbf{j},\) and \(\mathbf{w} = 5\mathbf{i} + 9\mathbf{j} - 4\mathbf{k}\) are coplanar.