Can someone help me understand how to rotate a vector A by some angle from vector B, both of size 512?

I have a feature vector that is compared to a basis vector which are the weights being updated, to do that an angle is calculated between the two vector’s and compared to ground truth. I would like reconstruct the feature vector by moving the basis vector by some angle, I’m not sure if rotation in higher dimensional space makes sense or if it’s better to try to learn that reconstruction