Special relativity - frames of reference

[qoqosz]

Homework Statement

We have two frames of reference: K (x,y,t) and K' (x',y',t') such that initially x=x'=y=y'=t=t'=0. Now let K' move with a velocity $$\vec{v} = v [\tfrac{1}{\sqrt{2}},\tfrac{1}{\sqrt{2}}]$$
Write Lorentz transformations in such a case.

Homework Equations

The Attempt at a Solution

My try is:
$$t' = \frac{t - (\vec{v} \circ (x, y))/c^2}{\sqrt{1 - \frac{v^2}{c^2}}}, \; x' = \frac{x - v_x t}{\sqrt{1 - \frac{v^2}{c^2}}}, y' = \frac{y - v_y t}{\sqrt{1 - \frac{v^2}{c^2}}}$$

where $$v_x = v_y = \frac{v}{\sqrt{2}}$$

 

[jambaugh]

Looks good to me.

 

[qoqosz]

Great, thank you!