Alright, so I split it up into two parts, r1 and r2.
Both have a magnitude of L / sqrt(2).
r1 has a direction vector of <√2 / 2, √2 / 2, 0>,
r2 has a direction vector of <√2 / 2, -√2 / 2, 0>.
Then, dl1 is <-L, 0, 0> and dl2 is <0, L, 0>.
Both cross products are L * (√2 / 2) in (-k) direction...