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Prove that a, b, c are non coplaner vectors if a*b, b+c, c+a are non coplaner vectors

Prove that a, b, c are non coplaner vectors if a*b, b+c, c+a are non coplaner vectors

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Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 years ago
Yes, in fact a +b is coplanar with both a and b⃗ . b+c is coplanar with both b c and c+a is coplanar with both c and a.
So, as there does not exist a common plane for all of the vectors, there cannot exist neither a common plane for vectors that are coplanar to each.

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