Suppose A represents a unit vector directed along the axis of rotation of a purely rotating body, and B is a unit vector directed along the velocity of a particle P of the body situated away from the axis. The value of A B is

Step-by-step solution

For a purely rotating body, the velocity v of any particle P situated away from the axis of rotation is given by v = r , where is the angular velocity vector and r is the position vector of the particle. The angular velocity vector is directed along the axis of rotation. From the properties of the cross product, the velocity vector v is perpendicular to both and r . Since A is a unit vector along the axis of rotation (parallel to ) and B is a unit vector along the velocity v , A is perpendicular to B . A B = | A |