As angular momentum, , therefore, the direction of is along a line perpendicular to the plane of rotation.

Angular momentum is a vector quantity that describes the rotational motion of an object. It depends on both the object's moment of inertia (a measure of its resistance to rotational motion) and its angular velocity (the rate at which it rotates). The direction of angular momentum is perpendicular to the plane of rotation and follows the right-hand rule.

The right-hand rule states that if you curl the fingers of your right hand in the direction of rotation, your thumb will point in the direction of the angular momentum vector. This means that the angular momentum vector is perpendicular to both the plane of rotation and the radius of the orbit.

To understand why the correct answer is option 'D' (line perpendicular to the plane of rotation), let's consider a rotating mass in a plane about a fixed point:

1. Angular Momentum Vector:
- Angular momentum is a vector quantity, which means it has both magnitude and direction.
- The direction of the angular momentum vector is given by the right-hand rule, as explained above.
- The vector points perpendicular to both the plane of rotation and the radius of the orbit.

2. Radius of Orbit:
- The radius of the orbit is simply the distance from the fixed point to the rotating mass.
- While the radius is involved in the calculation of angular momentum, it does not determine the direction of the angular momentum vector.

3. Tangent to the Orbit:
- The tangent to the orbit is a line that touches the orbit at a specific point.
- The tangent direction changes as the object rotates, but it does not determine the direction of the angular momentum vector.

4. Line Parallel to Plane of Rotation:
- This option is incorrect because the angular momentum vector is not parallel to the plane of rotation.
- It is perpendicular to the plane of rotation, as mentioned earlier.

5. Line Perpendicular to Plane of Rotation:
- This is the correct option because the angular momentum vector is indeed perpendicular to the plane of rotation.
- It is the result of the rotational motion and represents the axis of rotation.

In summary, the angular momentum of a mass rotating in a plane about a fixed point is directed along a line perpendicular to the plane of rotation. This direction is determined by the right-hand rule, and it is independent of the radius of the orbit or the tangent to the orbit.