# Why are we able to break a vector along it's components or in other words why is it that a vector exists along $x$, $y$ and $z$ axis?

Does a 3 d vector exist in three dimensions at once? It seems to me that a vector always changes axis along which it is to fit into the scenario. For example: Electric field in $x-y$ plane when passes through $y-z$ plane only uses it's $x$ component.

• Keep in mind that there is no universal definition of 'the axes'. I can chose a different set than you and we can still both work through to the same final physical results (though the coordinate values we use to express that result would be different). – dmckee Jun 11 '17 at 16:04
• everything is arbitrary in physics – Kavya Negi Jun 12 '17 at 10:52

Absolutely, a general vector is $$\vec r=x \hat i+y\hat j+z\hat k$$ in Cartesian coordinates. This vector has a component in each of the three dimensions and all components are mutually orthogonal. Since the vector $\vec r$ is equal to the sum of these 3 components then it must exist in three dimensions at once.