Shortest distance between two points moving with the same speed on two lines

Question

I have homework that I have to solve, and the my question is:
A cube has side length of 2 cm. One ant starts at corner A and travels to corner B.
Another ant starts at corner C and travels to corner D. The two ants leave at the same time and travel at the same speed. Find the shortest distance between the two ants.

and my solution:

I don't know if my answer is correct, is it?

Answer 1

The second ant is at $(2,2,-2t)$.

The squared distance is

$$(2t-2)^2+(-2)^2+(2t)^2=8(t^2-t+1).$$

By completing the square, the minimum is achieved at $t=\dfrac12$, when the ants are at the midpoints, and the distance is $\sqrt6$.