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let a,b,c be three non-coplanar vectors and d be a non-zero vector which is perpendicular to (a+b+c) and is represented as d=x(a × b)+y(b × c)+z(c × a) (× is cross product) Then prove that 1)x 3 +y 3 +z 3 =3xyz 2)xy+yz+xz≤0

let a,b,c be three non-coplanar vectors and d be a non-zero vector which is perpendicular to (a+b+c) and is represented as 
d=x(a × b)+y(b × c)+z(c × a)
(× is cross product)
Then prove that
1)x3+y3+z3=3xyz
2)xy+yz+xz≤0

Grade:12

1 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
6 years ago
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