# Mathematics - Vector

The vector comes with both direction and magnitude. The vector is expressed as an arrow along with the tail or head in mathematics. In Vector math, the length of the arrow signifies the magnitude of it. Vector represents the direction and magnitude, but it does not provide any information about where the force is applied on the Vector.

## The magnitude of a Vector

The vertical lines on both sides show the magnitude of Vector |a|. It represents the vector's length. The vector's magnitude is further calculated through Pythagoras theorem, i.e. |a| = √(x2+y2)

## Unit Vector

The length of the unit vector is equal to 1, and it shows the vector's direction. A Unit vector is also equal to the magnitude and vector's ratio. It is represented as a cap or hat (^). If a is a vector of arbitrary length and its magnitude is ||a||, then the unit vector is given by:

a^=a∥a∥

Some mathematical laws apply to vectors.

## Commutative Law:

In this, the vectors are added in any order. a + b = b + a

## Associative Law:

The associative law for vector addition states that when three or more vectors are added together, i.e.

(a + b) + d = a + (b + d)