$4.$ The figure below shows two spur gears mounted on shafts with bearing supports A$,$ B$,$ C$,$ D$.$ Assume gear $2$ is a $22$ tooth pinion driving the $49$ tooth gear $3.$ The metric gears have a module of $6$ mm and a $\backslash (20^\{\backslash$circ$\}\backslash )$ pressure angle. The shaft driving gear $2$ has an applied torque of $50$ Nm $.$

a$.$ Find the pitch diameters for the gears. Express your answer in mm$.$

b$.$ Find the tangent force $($torque force$)$ for the gears. Express your answer in N $.$

c$.$ Find the radial force $($spread force$)$ for the gears. Express your answer in N $.$