the unit vector in the direction of <1,3,2> is given by <1,3,2>/|<1,3,2>| = (1/14) <1,3,2>

the force in a certain direction is the magnitude of the force times the unit vector in that direction. so you get a vector in that direction with the magnitude of the force, which is what we want. so we take that vector to be our F

after that, it is just W = Force times Distance, but that translates into Work = the dot product of F and Displacement when dealing with vectors

W = (50/sqrt[14]) (1,3,2)·(2,-2,4)

= (50/sqrt[14]) (2-6+8)

= (50/sqrt[14]) (4)

= (200/sqrt[14])

= (200/14) (sqrt[14])

W = (100/7) (sqrt[14])

So if anyone could explain what's going on step by step it'd really help me.