证明曲面根号x+根号y+根号z=根号a的切平面在三坐标轴上的截距之和为常量

Question

如题所述

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.