The scalar product of two perpendicular vectors is

Explanation

Cos 90 is zero, so the dot product vanishes whenever the vectors are at right angles, and this is the standard test for perpendicularity. It is also why no work is done by a force acting at right angles to the displacement, such as the centripetal force on a body in circular motion. The dot product is maximum when the vectors are parallel and negative when the angle exceeds 90 degrees.