Vector Formula with multiple Equal signs?

[TastyLemons]

How do i go about solving the following equation? (Attached)

I am attempting to implement it into java. BUt i have not gotten any further than this:

wavenumber = new Vector2f(0.0f, 0.0f);
wavenumber.x = (float) (2 * Math.PI / wavelength);

Wikipedia Info for Equation:

In general, the angular wavenumber k (i.e. the magnitude of the wave vector) is given by

k = \frac{2\pi}{\lambda} = \frac{2\pi\nu}{v_\mathrm{p}}=\frac{\omega}{v_\mathrm{p}}
where \nu is the frequency of the wave, \lambda is the wavelength, \omega = 2\pi\nu is the angular frequency of the wave, and vp is the phase velocity of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber) is known as a dispersion relation.

SOURCE:

http://en.wikipedia.org/wiki/Wavenumber

 

[AlephZero]

It is just a short way of writing several different equations, $k = 2\pi/\lambda$, $k = 2\pi\nu/v_p$, $k = \omega/v_p$, etc.

In your computer program, use whichever equation(s) you need, depending on which values are known and which are unknown.

 

[TastyLemons]

So they are separate? i don't use them all together?