Question

Why two perpendicular vectors dont have effect on each other?

Answer 1

Suppose the 2 vectors are A and B, where A is in the x-axis, and B is in the y-axis.

Now see, if we take a component of A on B, we'll see, it's Acos ($\pi$/2). Now cos($\pi$/2) = zero. Since the component of A on B is zero, so, the component of forces acting along A will be zero, so it will have nil effect on B.
Hope this helps!