Q.1 Show that the Gallilean transformations leave the expression x + y + x + ct invariant whereas the same expression is not invariant under Lorentz transformations. Q.2 Show that the Lorentz transformations leave the expression x + y + 2-ct invariant. Q.3 By using a parameter a definded by tanh a v/c, show that the Lorentz transformation equations may be written as = x = x cosh act sinh a, y = y, z = z, ct' = ct cosha x sinh a.