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Math Help - Cross Product Help

  1. #1
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    Question Cross Product Help

    Find all the vectors u that satisfy the equation <1,1,1> X u = <-1,-1,2>




    (The answer in the back of the book is <u3-1, u3+1, u3> I just don't know how to get to it!)
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  2. #2
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    Re: Cross Product Help

    Hey jessicadowning.

    Do the know the formula for C = A X B where a = (a0,a1,a2), b = (b0,b1,b2) and c = (c0,c1,c2) where you get c0,c1, and c2 in terms of a0,a1,a2,b0,b1 and b2?
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  3. #3
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    Re: Cross Product Help

    No, I believe the process people are using for this problem is the determinant with the bottom vector being <u1, u2, u3>
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  4. #4
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    Re: Cross Product Help

    Yes that is equivalent (and generally how you do the calculation).

    So the determinant with u at the bottom and <1,1,1> in the middle gives

    i*(1*u3 - 1*u2) - j*(1*u3 - 1*u1) + k*(1*u2 - 1*u1) = <-1,-1,2>

    Now equating components gives you:

    u3 - u2 = -1
    u1 - u3 = -1
    u2 - u1 = 2.

    Row reducing this gives:

    >> A = [0, -1, 1, -1; 1, 0, -1, -1; -1, 1, 0, 2]
    A =

    0 -1 1 -1
    1 0 -1 -1
    -1 1 0 2

    >> rref(A)
    ans =

    1 0 -1 -1
    0 1 -1 1
    0 0 0 0

    So this means that u2 - u3 = 1 and u1 - u3 = -1. So we get

    u1 = u3 - 1
    u2 = u3 + 1

    So plug those in to the following:

    <u3 - 1, u3 + 1, u3> = U.
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  5. #5
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    Re: Cross Product Help

    Thanks!
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