Question: Let \(T\left( x,y,z \right)=100+{{x}^{2}}+{{y}^{2}}\) represents the temperature at each point on the sphere \({{x}^{2}}+{{y}^{2}}+{{z}^{2}}=50\). Find the maximum temperature on the curve formed by the intersection of the sphere and the plane \(x-z=0\)