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) (1,3,2) · (2,-2,4)
= (50/sqrt) (2-6+8)
= (50/sqrt) (4)
= (200/14) (sqrt)
W = (100/7) (sqrt)
So if anyone could explain what's going on step by step it'd really help me.