椭圆3X^2+2Y^2=12, Z=0. 绕Y轴旋转的旋转面在点M（0,根号3,根号2）处指向外侧的单位法向量为

Question

椭圆3X^2+2Y^2=12, Z=0. 绕Y轴旋转的旋转面在点M（0,根号3,根号2）处指向外侧的单位法向量为

Answer 1

椭圆3X^2+2Y^2=12,Z=0.绕Y轴旋转的旋转面为
3(X^2+Z^2)+2Y^2=12
F(x,y,z)=3(x²+z²)+2y²-12
旋转面在点外侧的单位法向量n∝(F'x,F'y,F'z)=(6x,4y,6z)
旋转面在点M（0,根号3,根号2）处指向外侧的单位法向量为
(0,√(2/5),√(3/5))