Lorentz transforms questions

[belette27]

1. Let's pretend that a particule with a relative speed V moves along a referential S (x; y and z)
   On that referential S, we measure this particule speed
   We then notice that particule has a speed on all 3 axes of that refrential S (x; y and z)
   Those speeds are then called Vx; Vy and Vz
   With those conditions, how would you write the lorentz transforms formula on the spatial (x;y and z) and temporal (T) coordinates?

   
   

   
   

   
   

[jimmyhelu]

The problem states that:

 

"Two events occur in an inertial system K as follows:

 

Event 1: x1 = a, t1 = 2a/c

Event 2: x2=2a; t2 = 3a/2c

 

In what frame K' will these events appear to occur at the same time? Describe the motion of system K'. "