Tuesday, March 07, 2006

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:

    Cx = Ax + Bx

    Cy = Ay + By

    Cz = Az + Bz

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

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

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