Special Theory of Relativity (Question 2 (20 Marks)) — UPSC Physics Optional CSE 2002 Paper I

An observer A sees two events at the same space point (\Delta x = \Delta y = \Delta z = 0) and separated in time by \Delta t = 10^{-6}\text{ s}. Another observer B sees them to be separated by \Delta t' = 3 \times 10^{-6}\text{ s}. What is the separation in space of the two events as observed by B? What is the speed of B relative to A?