Adding Vectors

To add two vectors, vector and vector, join the tail of one with the head of the other vector.

Adding Vectors

The vector sum equals the distance from the tail of the first vector to the head of the second vector.

 

Parallelogram Rule

Parallelogram Rule

If there are two vectors with a common origin and parallel lines to the vectors are drawn, a parallelogram is obtained whose diagonal coincides with the sum of the vectors.

To add two vectors, add their components.

Vector Components

Adding Vectors

Properties of Vector Addition

Associative.

Vector + (Vector + Vector ) = (Vector + Vector ) + Vector

Commutative.

Vector + Vector = Vector +

Additive identity.

Vector + Zero Vector =

Additive inverse or opposite.

Vector + (− Vector) = Zero Vector


Subtracting Vectors

Subtracting Vectors

To subtract two vectors Vector and Vector, add Vector with the opposite of Vector.