Question

Angle between 2 planes will be same as

• A. Angle between any 2 position vectors lying on the respective planes.
• B. Angle the line of intersection of planes makes with either of normal.
• C. Angle between the normals.
• D. None of these

Answer 1

The correct option is C Angle between the normals.

Case I If planes are not intersecting we know the direction vectors are free vectors so lets shift them for our convenience. Now you can see from property of right angled triangle that the angle between the normals will be same as the angle between the planes.

Case II when planes are parallel.

In this case both normal are collinear, the angle between them or normal to them will $0^{\circ }$ to ${180}^{\circ }$.

If you consider option A, you can see its value keeps changing as we change the vectors of our choice. Which is not consistent with the idea of angle between 2 planes as it is a constant value.

In case of option B, as the direction vector is a free vector you can shift it to meet the line of intersection and see it always makes an angle of ${90}^{\circ }$. In fact it’s always ${90}^{\circ }$ no matter what line you take on the plane.