To obtain the vector expression for the moment M₁ of F about λ, multiply the magnitude by the directional unit vector n to obtain

M_? = (r × F.n)n

Couple

The moment produced by two equal, opposite and non-collinear forces is called a couple.

We may also express the moment of a couple by using vector algebra. Referring to Fig. 1.6(a), the combined moment about point O of the forces forming the couple is

M = r_A × + r_R × (-F)= (r_A-r_R) ×F

where r_A and r are position vectors which run from point O to arbitrary points A and B on the lines of action of F and -F, respectively. Beacause r_A-r_B = r, we can express M as M = r × F

Here , the moment expression contains no reference to the moment center O and, therefore, is the same for all moment centers. Thus, we may represent M by a free vector, as shown in Fig. 1.6(b), where the direction of M is normal to the plane of the couple and the sense of M is established by the right-hand rule.