Question

Which is true?

(a) ∑F = ∑Fx + ∑Fy + ∑Fz

(b) ∑F = -(∑Fx + ∑Fy + ∑Fz)

(c) ∑F = ∑Fxi + ∑Fyj + ∑Fzk

(d) ∑F = -(∑Fxi+ ∑Fyj + ∑Fzk)

I got this question in quiz.

Origin of the question is Cartesian Vectors in chapter Force Vectors of Engineering Mechanics

Answer 1

Correct choice is (c) ∑F = ∑Fxi + ∑Fyj + ∑Fzk

Easiest explanation: The total of two or more forces is equal to the sum of their respective axis’s components. That is the resultant adds up all the components of the forces in their respective axis, whether it may be x, y or z axis.