Explain that angular velocity is a vector and its direction is given by the right-hand screw rule.

Angular velocity $(\vec{\omega})$ is defined as a vector quantity because it possesses both magnitude and a specific direction.
The direction of the angular velocity vector is determined by the right-hand screw rule: If you curl the fingers of your right hand in the direction of the rotation of the body, then the extended thumb points in the direction of the angular velocity vector $(\vec{\omega})$.
Alternatively, if a right-handed screw is rotated in the direction of the body's rotation, the direction in which the screw advances represents the direction of the angular velocity vector.
As shown in figure $(a)$, the angular velocity vector is always directed along the axis of rotation. For a body rotating in a counter-clockwise direction, the angular velocity is directed outwards (positive), and for a clockwise rotation, it is directed inwards (negative).