(Solved): Find the cross product \( \mathbf{a} \times \mathbf{b} \). \[ \mathbf{a}=\langle t, 5,1 / t), \quad ...

Find the cross product \( \mathbf{a} \times \mathbf{b} \). \[ \mathbf{a}=\langle t, 5,1 / t), \quad \mathbf{b}=\left\langle t^{2}, t^{2}, 1\right\rangle \] Verify that it is orthogonal to both \( \mathbf{a} \) and \( \mathbf{b} \). \[ \begin{array}{l} (\mathbf{a} \times \mathbf{b}) \cdot \mathbf{a}= \\ (\mathbf{a} \times \mathbf{b}) \cdot \mathbf{b}= \end{array} \]