Vectors

Technically, every vector $\mathbf{r}$ (the r standing for “radius” from the arbitrarily chosen origin) should be written in terms of basis vectors, e.g. $\mathbf{\hat{x}}$ , like so:

$\mathbf{r}=x\mathbf{\hat{x}}+y\mathbf{\hat{y}}+z\mathbf{\hat{z}}$

But in reality everybody knows about the basis vectors, and then can be assumed. You can write the same vector by omitting them — so long as you realize, conceptually, that they are implicit in the formula:

$\mathbf{r}=(x,y,z)$

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