(a) Event A happens at point (xA = 5, yA = 3, zA = 0) and at time tA given by ctA = 15; event B occurs at (10, 8, 0) and ct B = 5, both in system S.

(i) What is the invariant interval between A and B?

(ii) Is there an inertial system in which they occur simultaneously? If so, find its velocity (magnitude and direction) relative to S.

(iii) Is there an inertial system in which they occur at the same point? If so, find its velocity relative to S

(b) Repeat part (a) for A = (2, 0, 0), ct = 1; and B = (5, 0, 0), ct = 3.