Drawing Spacetime Diagrams: Quick Solutions

[schwarzschild]

Suppose you have an question like:

"In the t-x spacetime diagram of O, draw the basis vectors $$\vec{e}_0$$ and $$\vec{e}_1$$ Draw the corresponding basis vectors of $$\bar{O}$$, who moves with speed 0.6 in the positive x direction relative to O. Draw the corresponding basis vectors of $$\underline{O}$$, who moves with speed 0.6 in the positive x direction relative to $$\bar{O}$$."

I know how to solve this just by drawing the $$\bar{t}$$ axis and then drawing null lines from two points $$-a, a$$ finding where they intersect and drawing a line from that point through the origin. Anyways, I was just wondering if there was a quicker way to address such problems.

 

[utesfan100]

If you become more familiar with hyperbolic representations of the Lorentz transforms you can calculate these things with rapidity.

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