Question

Why angular displacement is scalar for large angles?

Answer 1

Angular displacement can't be a vector because addition is not commutative. Say we are looking at the earth with North America facing us and the North Pole facing up:if we rotate the earth so that we move 90 degrees north, now the NP is facing us and NA faces down. If we the rotate the earth to move 90 degrees east, we end up with NA facing down and the NP facing to the left. But, if we reverse the order, we end up facing the NP while NA faces to the the left. 

For very small displacements, however, the surface of the earth is basically flat, so "rotating" the earth is simply moving in a given direction without swapping any axis. So if we are facing some point A on the equator, either way we do the rotations we end up facing a point just NE of A, with the NP facing up.