To add two vectors, add their coordinates or components.

Given = (2, 1, 3), = (1, −1, 0) and = (1, 2, 3), find the vector = 2u + 3v − w.

= (4, 2, 6) + (3, −3, 0) − (1, 2, 3) = (6, −3, 3)

Given vectors and , determine the magnitude of the vector .

## Properties of Vector Addition

Associative.

+ ( + ) = ( + ) +

Commutative.

+ = +

Additive identity.

+ =

Additive inverse or opposite.

+ (− ) =

### Scalar Multiplication

The product of a number k by a vector is another vector:

In the same direction as if k is positive.

In opposite direction as if k is negative.

Of magintude .

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