XII Maths Chapter 10. Vector Algebra | Page 12

( xiii ) Vector Moment of a Force about a Point
The vector moment of torque M of a force F about the point O is the vector whose magnitude is equal to the product of | F | and the perpendicular distance of the point O from the line of action of F .
∴ M = r * F
where , r is the position vector of A referred to O .
( a ) The moment of force F about O is independent of the choice of point A on the line of action of F .
( b ) If several forces are acting through the same point A , then the vector sum of the moments of the separate forces about a point O is equal to the moment of their resultant force about O .
( xiv ) The Moment of a Force about a Line
Let F be a force acting at a point A , O be any point on the given line L and a be the unit vector along the line , then moment of F about the line L is a scalar given by ( OA x F ) * a