Question

If two forces magnitude F each are acting in the Cartesian coordinate and are acting at the points A(3,3) and B(-3,3). They are heading towards negative z direction and positive z direction respectively. The distance between them is given as r. The radius vectors of the force at A and B are Ra and Rb respectively. Then the moment is given as:

(a) (Ra-Rb).F

(b) (Rb-Ra).F

(c) (Ra-Rb)xF

(d) (Rb-Ra)xF

This question was addressed to me in examination.

This intriguing question comes from Moment of a Couple in portion Force System Resultants of Engineering Mechanics

Answer 1

Right answer is (d) (Rb-Ra)xF

The explanation: The moment of a couple as we know is the cross product of the force and the distance between them. But in this case, we are given the radius vectors of the forces. So when we apply the vector maths to find the distance between the forces we get that the distance r = Rb-Ra. Now that we have the distance, we cross it with the force.