Please answer step by step.

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

The magnitude of the magnetic field at a certain distance from a long, straight conductor is represented by b. what is the magnitude of the magnetic field at twice the distance from the conductor? a. at twice the distance, the magnitude of the field is 4b. b. at twice the distance, the magnitude of the field is 2b. c. at twice the distance, the magnitude of the field is b/2.d. at twice the distance, the magnitude of the field is b/4.e. at twice the distance, the magnitude of the field remains equal to b.

A1.5m wire carries a 2 a current when a potential difference of 52 v is applied. what is the resistance of the wire?