PhysicsClassical Physics

The Vector Sum of Two or More Vectors Is Called What?

Name the vector sum of two or more vectors and see how a resultant represents their combined magnitude and direction.

Question

What is the vector sum of two or more vectors called?

Answer

It is called the resultant vector, or simply the resultant.

If several vectors are A1,A2,,An\mathbf A_1,\mathbf A_2,\ldots,\mathbf A_n, their resultant is

R=A1+A2++An.\mathbf R=\mathbf A_1+\mathbf A_2+\cdots+\mathbf A_n.

The resultant is a vector, so it has both magnitude and direction. It represents the single vector with the same combined effect as the vectors being added. In component form,

Rx=iAi,x,Ry=iAi,y,Rz=iAi,z.R_x=\sum_i A_{i,x},\qquad R_y=\sum_i A_{i,y},\qquad R_z=\sum_i A_{i,z}.

If the component sums all equal zero, the resultant is the zero vector.

Evidence boundary

The question asks for the name of the vector sum and supplies no numerical vectors. This answer therefore defines the resultant but does not invent a magnitude, direction, diagram, or component values.

Sources

These references support the concepts and methods used in the explanation above.