Question

The direction of the area vector is perpendicular to the plane is rotated about an axis lying in the plane of the given plane, then the direction of area vector:
(A) Does not change.
(B) Remains the same.
(C) May not be changed.
(D) None of the above.

Answer 1

Hint: We know that with the change in direction of the plane the orientation of the plane also changes and this will change the direction of the area vector accordingly.

Complete step by step answer
It is given in the question that the direction of the area vector is perpendicular to the plane which is rotating about an axis lying in the plane of the given plane, then we have to find the change in the area vector.
It is noted that when the plane is rotating about the axis which is lying in the same plane then the orientation of the plane keeps on changing and therefore, we can say that if orientation changes then the direction of the area vector will also change accordingly.
Therefore, with the change in the direction of the plane the direction of the area vector will also change.
In options, A and option B is wrong because we know that the direction of the area vector will change with the change in direction of the plane. Similarly, option C is also wrong because the direction of the area vector will surely change.

Thus, option D none of the above is the correct answer.

Additional information
It is noted that the area is not a vector. But it can be represented as a vector in three-dimensional situations. In the actual area is scalar in a three-dimensional situation it is treated as a vector whose direction is perpendicular to the plane.

Note
Here the normal unit vector associated with the area vector gives only the direction and not the magnitude. The direction is perpendicular to the plane.
One can make mistakes. They may assume that the direction id changing but the plane is constant so, the area vector will also remain constant i.e., it will not change, but we know that change in direction will change the direction of the plane and this will change the direction of the area vector.