In a large laboratory a projectile (mass 0.25 mg, charge 4.0 microC), now moving with a velocity of 600m/s due north, feels a magnetic force now of 8.4 mN east. Nearby, a beam of protons is traveling steadily at 400 m/s at 36.9 degrees north of up. Throughout this region there is a uniform magnetic field while all other forces are negligible; determine that vector magnetic field.