# Thread: Can't figure out this 3d vectors problem.

1. ## Can't figure out this 3d vectors problem.

I've been trying to figure out how my teacher did this work question from a note she gave us, for two hours now and I still can't figure it out. If one of you guys could explain to me what she's doing I'd be real grateful.

Anyways,

A 50N force acting in the direction (1,3,2) moves an object from A(2,3,-1) to B(4,1,3).

AB = distance = (4-2,1-3,3-(-1)
= (2,-2, 4)

Force is 50N along (1,3,2).

F = 50(1/sqrt[14]) (1,3,2) *Really don't understand what's going on here

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.

I've been trying to figure out how my teacher did this work question from a note she gave us, for two hours now and I still can't figure it out. If one of you guys could explain to me what she's doing I'd be real grateful.

Anyways,

A 50N force acting in the direction (1,3,2) moves an object from A(2,3,-1) to B(4,1,3).

AB = distance = (4-2,1-3,3-(-1)
= (2,-2, 4)

Force is 50N along (1,3,2).

F = 50(1/sqrt[14]) (1,3,2) *Really don't understand what's going on here
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

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.
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