设F(x,y,z)=x2-y2-3z 则Fx(x,y,z)=2x,Fy(x,y,z)=-2y,Fz(x,y,z)=-3 Fx(2,-1,1)=4,Fy(2,-1,1)=2,Fxz(2,-1,1)=-3 曲面x2-y2-3z=0上点(2,-1,1)处的切平面方程为4(x-2)+2(y+2)-3(z-1)=0 法线方程是(x-2)/4=(y+2)/2=(z-1)/(-3)