Consider a 3 × 3 real symmetric matrix S such that two of its eigenvalues are a ≠ 0, b ≠ 0 with respective eigen vectors \(\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right],\left[ {\begin{array}{*{20}{c}} {{y_1}}\\ {{y_2}}\\ {{y_3}} \end{array}} \right]\).

If a ≠ b then x₁y₁ + x₂y₂ + x₃y₃ equals