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Prove that for any two vectors vec(a) an...

Prove that for any two vectors `vec(a)` and `vec(b), vec(a).(vec(a)xx vec(b))=0`. Is `vec(b).(vec(a)xx vec(b))=0` ?

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The correct Answer is:
Yes
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Knowledge Check

  • If vec(b) and vec(c) are two non-collinear vectors such that vec(a) || (vec(b) xx vec(c)) , then (vec(a) xx vec(b)).(vec(a) xx vec(c)) is equal to

    A
    `vec(a)^(2) (vec(b).vec(c))`
    B
    `vec(b)^(2)(vec(a).vec(c))`
    C
    `vec(c)^(2) (vec(a).vec(b))`
    D
    none of these

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