Applying Rotation to a Movement Vector

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I started writing a 3D Engine that uses x/z and y/z to create depth. I also added a list that checks the last element to see if it is W, A, S, or D (W=1,A=2,S=3,D=4). Currently, if you rotate the character to the left and enter W, they move to the right. In my previous 3D Engines I would just normalize the vector and mulitply it by a Vec3(0,0,1). However, trying this in Desmos just breaks everything? How do I apply rotation to my movement vector in Desmos so that pressing W always moves the player in the direction they are facing?

Basic 3D

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AppliedRotation

I found the fix! It was actually quite straightforward, I have provided an image if anyone else is interested in creating something similar.

Thanks!

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