A body is rotating uniformly about vertical axis fixed in an inertial frame. The resultant force on a particle of the body not  on the axis is

Since angular velocity of the body is constant ,its angular acceleration must be zero.

Therefore trangential acceleration and hence tangential force acting on the particle must be zero.

So, the resultant force acting on particle must be radially inward and hence this force intersects the axis of rotation and perpendicular to the axis of rotation.