- #1

dingo_d

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## Homework Statement

This seems like a trivial question (because it is), and I'm just not sure if I'm doing it right.

I have vector in cartesian coordinate system:

[tex]\vec{a}=2y\vec{i}-z\vec{j}+3x\vec{k}[/tex]

And I need to represent it in cylindrical and spherical coord. system

## Homework Equations

[tex]a_\rho=a_x\cos\phi+a_y\sin\phi[/tex]

[tex]a_\phi=-a_x\sin\phi+a_y\cos\phi[/tex]

[tex]a_z=a_z[/tex]

## The Attempt at a Solution

What is cofusing me is this:

The formula for [tex]\phi[/tex] is[tex]\phi=\arctan\frac{y}{x}[/tex]. Are those x and y in fact [tex]a_x[/tex] and [tex]a_y[/tex]?

By some kind of reasoning it should be. But then [tex]\phi[/tex] is [tex]\phi=\arctan\frac{-z}{2y}[/tex] :\

Is this correct? And do I need to change the unit vectors too?