Question

is a vector is changed when rotated through an angle of 360 degree?

Answer 1

No the vector do not change if rotated through an angle 360⁰. 360⁰ is actually a full rotation. The vector comes back to the same position after a full rotation. Neither its magnitude nor its direction will be different from the original after 360⁰ rotation. So, it will be same as the original vector.