A particle of mass m, with charge q > 0, in a uniform magnetic field B = BZ parallel to the z axis . the particle is in a medium where a velocity v results in a friction force F = -kv where k > 0 is a constant coefficient of friction. a) If x(t = 0) = x0, y(t = 0) = y0, z(t = 0) = z0, vx(t = 0) = v0,x, vy(t = 0) = 0, vz(t = 0) = v0,z, t = m/k, w = qB/m and tan(ß) = wɩ. What are the equations of motion in x, y and z? T Show detailed calculations to prove X = (t)Vo,x cos (Beta) e^-t/τ cos (wt + Beta) + Xo + τ cos^2 (Beta) Vo,x Y = (t) Vo,x cos (Beta) e^-t/t sin (wt + Beta) + Yo - τ cos (Beta) sin (Beta) Vo,x Z = Zo + T Vo,z (1 − e^-t/t) there are t variables for time and the other T is greek tau which is defined above.