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If bara,barb,barc are non-coplaner, then...

If `bara,barb,barc` are non-coplaner, then show that the vectors `bara -bar b , barb + barc ,bar c + bara` are coplanar

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The correct Answer is:
Hence, the given vectors are coplanar.
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If bara,barb,barc are non-coplanar vectors, prove that barb xx barc, barc xx bara, bara xx barb are also non coplanar and hence express any vector bard in terms of the vectors barbxxbarc, barcxxbara , and baraxxbarb .

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Knowledge Check

  • [bara barb barc]+[bara barc barb] =

    A
    `[bara barb barc]`
    B
    `2[bara barb barc]`
    C
    `3[bara barb barc]`
    D
    0
  • If bara, barb, barc are non-coplanar, nonzero vectors and barr is any vector in space then [bara barb barc]barc+[barb barc bara]bara+[barc bara barb]barb =

    A
    `3[barabarbbarc]barr`
    B
    `[barabarbbarc]barr`
    C
    `[barabarbbarc]`
    D
    `bar0`
  • If bara, barb, barc are three non-coplanar vectors, barp=(barbxxbarc)/([bara barb barc]),barq=(barcxxbara)/([bara barb barc]),barr=(baraxxbarb)/([bara barb barc]) then (bara+barb).barp+(barb+barc).barq+(barc+bara).barr =

    A
    0
    B
    6
    C
    3
    D
    `-4`
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