Let the vectors $\mathbf{a}$ and $\mathbf{b}$ be specified by
$$\mathbf{a} = -3\mathbf{e_1} + 2\mathbf{e_2} - 8\mathbf{e_3}$$
$$\mathbf{b} = 5\mathbf{e_1} - 7\mathbf{e_2} + 3\mathbf{e_3}$$
where $\{\mathbf{e_i}\}$ is an orthonormal basis. Evaluate the expression:
$$\Psi = \frac{a_ib_ia_jb_j - a_ka_kb_lb_l}{a_ma_m}$$
Please help me here. How can we utilize $\mathbf{e_1}, \mathbf{e_2}, \mathbf{e_3}$ vectors here to find the value. I have no idea as how to proceed.