a) A single charged positive ion moves with a velocity of(2i+j-k) 10^3 m/s in a region of space where the magnetic field is given as (0.6i +0.8j-0.4k) T. Discover the magnitude of the magnetic force exerted on the ion.
b) A proton (charge, +e = 1.6 x 10^-19 C), moving at a speed of 3 x 10^5 m/s in a magnetic field, feels a zero force when this proton moves horizontally toward the south. But, the proton experiences a horizontal force of 6.0 x 10^-14 N in a direction toward the east when it moves vertically downward inside the field. Discover the magnitude and direction of the magnetic field in the region.