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Manipal MET2020MathematicsVector Algebra

If a , b and c are three non-coplanar vectors, then [ a b b c c a ] is equal to

Options

  1. A[ a b c ]^3
  2. B[ abc ]^2
  3. C0
  4. DNone of these

Correct answer

B. [ abc ]^2

Step-by-step solution

[a b b c c a] aligned & =(a b) [(b c) (c a)] & =(a b) [((b c) a) c-((b c) c) a] & =(a b) ([b c a] c-[b c c] a) & =(a b c)[b c a]-[a b a] 0 & =[a b c][a b c]-0=[a b c]^2 aligned

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