Then use cosine formula to calculate

Connect AC and BD, and the intersection point is O.

Move A 1B 1 to A 1O in parallel.

Then A 1C and A 1O are the two sides of the triangle line A 1OC.

The angle CA 1O is the angle formed by A 1C and DE.

Using cosine formula

Cos angle ca1o = (a1c 2+a1o 2-oc2)/2 * a1c * a1o = two thirds of the root number two.

I don't understand the vector method, and I don't understand why the answer is different from the one upstairs. I hope you can verify these two methods yourself.