If x + y + z = 0, then what is the value of $$\frac{{xy + yz + zx}}{{{x^2} + {y^2} + {z^2}}}?$$

Solution (By Examveda Team)

Given, x + y + z = 0
By putting values x = 2, y = -1, z = -1
$$\eqalign{ & {\text{Now, }}\frac{{xy + yz + zx}}{{{x^2} + {y^2} + {z^2}}} \cr & = \frac{{ - 2 + 1 - 2}}{{4 + 1 + 1}} \cr & = \frac{{ - 1}}{2} \cr} $$