If x = 997, y = 998 and z = 999 then the value of x2 + y2 + z2 - xy - yz - zx is?

Answer: Option D

$$\begin{array}{rl}& x^2+y^2+z^2-xy-yz-zx\\ & =\frac{1}{2}\left[{\left(x-y\right)}^2+{\left(y-z\right)}^2+{\left(z-x\right)}^2\right]\end{array}$$
  $$=\frac{1}{2}$$ $$\left[{\left(997-998\right)}^2+{\left(998-999\right)}^2+{\left(999-997\right)}^2\right]$$
$$\begin{array}{rl}& =\frac{1}{2}\left(1+1+4\right)\\ & =3\end{array}$$