1. ## Vector Calculus

A quick question. I'm trying to deduce what the following basis are:
$-z\hat{j} + y\hat{k}$

And

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

I know for instance

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

But how would i deduce the first two?

Thanks

2. ## Re: Vector Calculus

These symbols mean nothing if you don't give them a meaning by defining them.

3. ## Re: Vector Calculus

Well i, j and k are the basis that translate to x, y, z.

a_r and a_phi are the basis for polar coordinates i believe.

4. ## Re: Vector Calculus

Then your problem makes no sense. Your $\hat{i}$, $\hat{j}$, and $\hat{k}$ are three dimensional while $\hat{a_r}$ and $\hat{a_\phi}$ are two dimensional. You will have to complete that by using cylindrical coordinates ir spherical coordinates.