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Math Help - Problem with vectors

  1. #1
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    Problem with vectors

    Question

    Forces of magnitude 3 Newtons, 5 Newtons and 7 Newtons act along the vectors (-3,-2,-9) (8,5,-9) (4,-1,-9)

    Find the x component.

    I have the answer at 4.968 however i can not arrive at it, attached is my working out. d has been used instead of c.


    i have the x components as 2.531, -2.774 and -6.93 however these are not correct as they do not equal the answer of 4.968

    Thanks
    Attached Thumbnails Attached Thumbnails Problem with vectors-working.png  
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  2. #2
    Super Member ebaines's Avatar
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    Re: Problem with vectors

    You need to find the x-component of each of the three force vectors, then add them. So starting with 3 N acting along (-3, -2, -9): the magnitude of this directional vector is sqrt(3^2+2^2+9^2) = 9.969, and the portion acting in the x direction is -3/9.969 = -0.3094. Multiply by 3N to get -0.928N. This is the amount fo force acting in the x-direction for the 3N force. Repeat this for the other two vectors and add, and you should get Fx = -0.928N + 3.068N +2.828N = 4.968N.
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  3. #3
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    Re: Problem with vectors

    ah this looks right, thank you. Can i ask why the -3 is divided by 9.969?
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  4. #4
    Super Member ebaines's Avatar
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    Re: Problem with vectors

    What you really want is the directional vectors to be expressed as unit vectors (i.e. have magnitude 1). So that first directional vector is given as (-3, -2, -9) expressed as a unit vector is (-3/9.696, -2/9.969, -9/9.969), or (-0.3094, -0.2063, -0.9283). You should double check that this has magnitude of 1. Now you can multiply the x, y, and z components of this unit vector by 3 N to find the x, y, and z components of the 3N force.
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  5. #5
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    Re: Problem with vectors

    Thanks ebaines, cleared that up for me
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  6. #6
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    Re: Problem with vectors

    Hi Ebaines, is it possible for you to give me some help to get started on another question.

    Three vectors

    a = xi - 3j + 9K
    b = -3i + xj - 10K
    c = 9i - 10j + xk

    Find the largest value of x for which the magnitude of the resultant is equal to 17.
    I am given the correct answer of 8.564 but i dont know how to get that.

    I have no working out to show for this as i dont know where to start, but some advice would be helpful

    Thanks
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  7. #7
    Super Member ebaines's Avatar
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    Re: Problem with vectors

    When you add vectors a, b and c the resultant is ((x-3+9)i, (-3+x-10)j, (9-10+x)k). Now write out the formula for the magnitude of this vector, and solve for x such that the magnitude is 17.
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