# What is meant by a component of a vector?

Sep 26, 2014

Consider a vector $\vec{v}$, for example, in space:

If you want to describe it to, say, a friend you can say that has a "modulus" (=length) and direction (you may use, for example, North, South, East, west...etc.).

There is also another way to describe this vector.
You must take your vector into a reference frame to have some numbers related to it and then you take the coordinates of the tip of the arrow...your COMPONENTS !
You can now write your vector as: $\vec{v} = \left(a , b\right)$

For Example: $\vec{v} = \left(6 , 4\right)$

In 3 dimensions you simply add a third component on the $z$ axis.
For example: $\vec{w} = \left(3 , 5 , 4\right)$