Question

证明曲面根号x+根号y+根号z=根号a (a大于0)上任何点处的切平面在各坐标轴...

Answer 1

法向量n=(Fx,Fy,Fz)=(1/2√x,1/2√y,1/2√z)

则任意一点,设为(x0,y0,z0)的切平面为1/2√x0(x-x0)+1/2√y0(y-y0)+,1/2√z0(z-z0)=0

截距分别为,√a*√x0,√a*√y0,√a*√z0

√a*√x0+√a*√y0+√a*√z0=√a*(√x0+√y0+√z0)=√a*√a=a

证毕.