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# Unit Vectors / Basis Vectors
In the $$xy$$-coordinate system, there are two special vectors.
* The one pointing to the right with length $$1$$, commonly called “i hat” $$\hat{i}$$ or “the unit vector in the x-direction”.
* The other one is pointing straight up with length $$1$$, commonly called “j hat” $$\hat{j}$$ or “the unit vector in the y-direction”.
### Choosing different basis vectors
Consider a random pair of vectors, $$\vec{v}$$ and $$\vec{w}$$.
$$a\vec{v} + b\vec{w}$$
The linear combination of two vectors can be used to describe ***every*** possible two-dimensional vector.
So while we can use a random pair of vectors as basis vectors, forming a new coordinate system, the association would be different from the version using the standard basis of $$\hat{i},\hat{j}$$
