Lines & Planes in Space · Challenge problem

Let $L_1$ be the line $\mathbf r_1(t) = (0, 0, 1) + t\langle 1, 1, 1\rangle$ and $L_2$ the line $\mathbf r_2(s) = (3, 0, 0) + s\langle 1, -1, 0\rangle$. Find the $z$-coordinate of the point of $L_1$ that is closest to $L_2$.