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Math Help - Can't figure out this 3d vectors problem.

  1. #1
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    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.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by zerobladex View Post
    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
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