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Math Help - General solution of vector equation

  1. #1
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    General solution of vector equation

    Find the general solution of the vector equation:
    u \times(i-3k)=2j

    I've got one more question similar, so i need some pointers.
    Thanks!
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  2. #2
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    Quote Originally Posted by arze View Post
    Find the general solution of the vector equation:
    u \times(i-3k)=2j

    I've got one more question similar, so i need some pointers.
    Thanks!
    Substitute u = ai + bj + ck. Note that u.(2j) = 0 and so b = 0. So u = ai + ck. Substitute and solve for a and c. (Note that the cross-product gives one equation and you can get another equation by equating magnitudes).
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    I don't understand how u.(2j) = 0.
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  4. #4
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    Ok got the part about b=0.
    I found that 3a+c=2
    I don't know what else.
    The answer is u=2k+t(i-3k) where t is a scalar, i think
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  5. #5
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    Quote Originally Posted by arze View Post
    Ok got the part about b=0.
    I found that 3a+c=2
    I don't know what else.
    The answer is u=2k+t(i-3k) where t is a scalar, i think
    Calculate (ai + ck) x (i - 3k) and equate the result to 2j.
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  6. #6
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    I found 3a+c=2, i need another equation of a and c?
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  7. #7
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    ux(i-3k) is a vector- it has i, j, and k components. Setting the i component equal to 0, the j component equal to 2 and the k component equal to 0 gives you three equations for the three coefficients of i, j, and k in u.
    Last edited by mr fantastic; June 21st 2010 at 01:22 PM.
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  8. #8
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    Quote Originally Posted by arze View Post
    I found 3a+c=2, i need another equation of a and c?
    Go back and read post #2 more carefully.
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    Really sorry, but I can't get it, you said from the magnitudes? How do I find that?
    Sorry I don't understand
    Thanks
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  10. #10
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    Quote Originally Posted by arze View Post
    Really sorry, but I can't get it, you said from the magnitudes? How do I find that?
    Sorry I don't understand
    Thanks
    If the answer has a parameter (t) in it, then you don't need another equation. Just get c in terms of a, say, and substitute into u = ai + ck.

    Otherwise, (and I haven't checked whether the equation is different) equate the magnitude of each side of (ai + ck)(i-3k)=2j (I assume you know how to find the magnitude of a vector).
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