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Math Help - Vector question.

  1. #1
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    Vector question.

    Find u such that the vectors i + j - k, 2i - j + k and ui - j + uk are coplanar.
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  2. #2
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    Solve \left\langle {u, - 1,u} \right\rangle  \cdot \left[ {\left\langle {1,1, - 1} \right\rangle  \times \left\langle {2, - 1,1} \right\rangle } \right] = 0 for u.
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  3. #3
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    Or: three vectors are co-planar if any one of them can be written as a linear combination of the other two.

    Find a u such that a(i + j - k)+ b(2i - j + k)= ui - j + uk for some a and b. That is, a+ 2b= u, a- b= -1, -a+b= u. You can solve the first and second equations for a and u in terms of b, then find b so that the second equation is satisfied.
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