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 that1)x3+y3+z3=3xyz2)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