切平面与法线 求切平面和法线
\u66f2\u7ebf\u7684\u5207\u5e73\u9762\u4e0e\u6cd5\u7ebf\u6c42\u504f\u5bfc
zx=2x
zy=6y
\u6240\u4ee5,(1,1,3)\u5904\u7684\u6cd5\u5411\u91cf\u4e3a
(zx,zy,-1)=(2,4,-1)
\u5207\u5e73\u9762\u65b9\u7a0b\u4e3a
2(x-1)+4(x-1)-(x-3)=0
\u5373\u4e3a
2x+4y-z-3=0
\u6cd5\u7ebf\u65b9\u7a0b\u4e3a
(x-1)/2=(y-1)/4=(z-3)/(-1)
\u6c42\u504f\u5bfc
zx=2x
zy=6y
\u6240\u4ee5,(1,1,3)\u5904\u7684\u6cd5\u5411\u91cf\u4e3a
(zx,zy,-1)=(2,4,-1)
\u5207\u5e73\u9762\u65b9\u7a0b\u4e3a
2(x-1)+4(x-1)-(x-3)=0
\u5373\u4e3a
2x+4y-z-3=0
\u6cd5\u7ebf\u65b9\u7a0b\u4e3a
(x-1)/2=(y-1)/4=(z-3)/(-1)
（水平面与其交线是椭圆，竖平面若与其相交则交线是抛物线）；
令 F=x²/4+y²/9 -z，该曲面的法线方向数可表示为 {∂F/∂x,∂F/∂y,∂F/∂z} 即 {x/2,2y/9,-1}；
点 (-2,-3,2) 处的切平面法线方向数：{-1,-2/3,-1} （或{1,2/3,1}）；
指定点处切平面方程：(x+2)+2(y+3)/3+(z-2)=0，化简后：3x+2y+3z+6=0；
对应法线方程：(x+2)=3(y+3)/2=(z-2)；
绛旓細绌洪棿鏇查潰鐨鍒囧钩闈㈠拰娉曠嚎.璁剧┖闂存洸闈㈢殑鏂圭▼涓 锛孎(x,y,z)=0锛岃岃孧(x0,y0,z0)鏄洸闈⑽ｄ笂鐨勪竴鐐.娉曞悜閲忥細(Fx(x0,y0,z0),Fy(x0,y0,z0),Fz(x0,y0,z0)).娉曠嚎鏂圭▼锛歺−x0Fx(x0,y0,z0)=y−y0Fy(x0,y0,z0)=z−z0Fz(x0,y0,z0).鍒囧钩闈㈡柟绋嬶細Fx(x0,y0,...
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