A quick question. I'm trying to deduce what the following basis are:

$\displaystyle -z\hat{j} + y\hat{k} $

And

$\displaystyle x\hat{k} - z\hat{i}$

I know for instance

$\displaystyle x\hat{i} + y\hat{j} = {\hat{a}}_{r}r$

$\displaystyle -y\hat{i} + x\hat{j} = {\hat{a}}_{\phi}r$

But how would i deduce the first two?

Thanks