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Math Help - Can someone explain this to me?

  1. #1
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    Exclamation Can someone explain this to me?

    Find the values of x such that the given vectors are orthogonal. (Enter your answers from smallest to largest.)
    xi + 3xj
    xi - 5j

    x = _______ (smaller value)
    x = _______ (larger value)

    The answer is 0 and 15, but how do I get that?
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  2. #2
    MHF Contributor chisigma's Avatar
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    Let's consider the two vectors as two complex numerrs...

    z_{1} = x + 3 x i

    z_{2} = x - 5i

    ... where i = \sqrt{-1} is the 'imaginary unit'. The condition of orthogonality is...

    Re\{\frac{z_{1}}{z_{2}}\} = 0

    ... that leads at the algebraic equation...

    x^{2} - 15 x=0

    ... whose solution are x=0 and x=15 ...

    Kind regards

    \chi \sigma
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  3. #3
    Junior Member woof's Avatar
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    They are orthogonal if, when you dot them, you get zero. So that gives you an equation to solve for x:

    (xi + 3xj)\cdot (xi - 5j)=x^2-15x=0

    Now solve that by factoring.
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  4. #4
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    Thanks guys!
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