Answer should be $0.$

“Eigen-vectors of a real symmetric matrix are orthogonal(perpendicular).”

So, here matrix $A$ is symmetric because $A^T = A.$

So, $x_{1} \perp x_{2}$ (or) $x_{1}^{T} x_{2}=0$ (or) $\vec{x_{1}}.\vec{x_{_{2}}} = 0$ i.e. $(70\hat{i}+(\lambda_{1}-50 )\hat{j}).((\lambda_{2}-80 )\hat{i}+70\hat{j})=0$ i.e $70(\lambda _{2}-80) + 70(\lambda _{1}-50)=0$