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Math Help - Findind a vector d

  1. #1
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    Findind a vector d

    Let \mathbf{\overrightarrow{a} = i + j -2k } , \mathbf{\overrightarrow{b} = 2i + j + k} and \mathbf{\overrightarrow{c} = 4i + j - 2k} . Find a vector \mathbf{\overrightarrow{d}} such that \mathbf{\overrightarrow{d} \times \overrightarrow{b} = \overrightarrow{c} \times \overrightarrow{b}} and \mathbf{\overrightarrow{d} . \overrightarrow{a}}=0.
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  2. #2
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    Vector and scalar product

    Hello varunnayudu
    Quote Originally Posted by varunnayudu View Post
    Let \mathbf{\overrightarrow{a} = i + j -2k } , \mathbf{\overrightarrow{b} = 2i + j + k} and \mathbf{\overrightarrow{c} = 4i + j - 2k} . Find a vector \mathbf{\overrightarrow{d}} such that \mathbf{\overrightarrow{d} \times \overrightarrow{b} = \overrightarrow{c} \times \overrightarrow{b}} and \mathbf{\overrightarrow{d} . \overrightarrow{a}}=0.
    Suppose that d = pi + qj + rk. Then equate the coefficients of i, j and k in vector products:

    q - r = 3

    2r - p = -8

    p - 2q = 2

    (Do you see where these equations come from?)

    These equations are not all independent. You can't solve for p, q and r yet. But you also know that d.a = 0. So you also have:

    p + q - 2r = 0

    Now you can solve for p, q and r.

    Grandad
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