If x, y, z are not all zero & if ax + ...

If `x, y, z` are not all zero & if `ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0`, then prove that `x: y : z = 1 : 1 : 1` OR `1 :omega:omega^2 OR 1:omega^2:omega` , where `omega` is one ofthe complex cube root of unity.

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If `x, y, z` are not all zero & if `ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0`, then prove that `x: y : z = 1 : 1 : 1` OR `1 :omega:omega^2 OR 1:omega^2:omega` , where `omega` is one ofthe complex cube root of unity.

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