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

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

**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.

### Properties of Vector Addition

Associative.

+ ( + ) = ( + ) +

Commutative.

+ = +

Additive identity.

+ =

Additive inverse or opposite.

+ (− ) =

### Subtracting Vectors

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

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