Vector Addition

Definition, Cummutative and Associative Laws

The sum of two vectors, written C=A+B, is defined as the vector that results from following vector A to its head and then placing vector B's tail at the head of A and following it in turn.

In Cartesian coordinates, this sum is particularly straightforward:

C_x = A_x + B_x

C_y = A_y + B_y

C_z = A_z + B_z

Vector addition is commutative and associative: the order of addition is generally irrelevant:

A + B = B + A(A + B)+ C = A + (B+C)