已知空间曲面的方程怎样设在任意点的切平面方程？
曲面上一点(x,y,z)处的法向量为n=(x/2,2y,2z/9)
把点p带入得到n=(1,
-2,
2/3)
可以取n0=(3,
-6,
2)
所以切平面为3(x-2)-6(y+1)+2(z-3)=0
整理后3x-6y+2z=18
法线为(x-2)/3=(y+1)/(-6)=(z-3)/2
满意请采纳，谢谢支持。
绛旓細璁绌洪棿鏇查潰鏂圭▼涓篎(x,y,z)=0 閭ｄ箞瀹冨湪鐐(x0,y0,z0)澶勭殑鍒囧钩闈㈢殑娉曞悜閲忓彲浠ヨ〃绀轰负 n0=(F'x(x0,y0,z0),F'y(x0,y0,z0),F'z(x0,y0,z0))鎵浠ュ垏骞抽潰鏂圭▼涓 F'x(x0,y0,z0) (x-x0)+F'y(x0,y0,z0) (y-y0)+F'z(x0,y0,z0) (z-z0)=0 ...
绛旓細绌洪棿涓鏇查潰銆戜竴鑸柟绋嬮氬父銆愬彧鐢ㄤ竴涓戞柟绋嬶紱绌洪棿涓殑銆愭洸绾裤戜竴鑸柟绋嬫墠閫氬父銆愮敤涓や釜銆戞柟绋嬭仈绔嬨備絾鑻ユ槸 銆愬弬鏁版柟绋嬨戯紝鍒欐儏鍐典緥澶栵紝浼氬鍑轰竴浜涙柟绋嬨傚锛氱悆蹇冨湪鍘熺偣鐨勭悆闈㈡柟绋 x^2+y^2+z^2=r^2 銆愪竴涓氨澶熶簡銆憍oy骞抽潰涓婄殑鍦鐨勬柟绋锛堟洸绾匡級 x^2+y^2=r^2 z=0 銆愪袱涓仈...
绛旓細璇佹槑锛涗护f锛坸锛寉锛寊锛=d2=(x?x0)2+(y?y0)2+(z?z0)2+位F锛坸锛寉锛寊锛夛紝瑕佷娇S涓婄殑鐐筈浣垮緱绾挎P0Q鏄疨0涓嶴涓浠绘剰涓鐐硅繛绾跨殑鏈鐭嚎娈碉紝F锛坸锛寉锛寊锛夋槸鍏夋粦鏇查潰锛庡張鏍规嵁甯歌瘑鍒嗘瀽鐭ワ紝f锛坸锛寉锛寊锛夊湪Q澶勫彇寰楁瀬鍊肩偣灏辨槸鏈鍊肩偣锛庣敤鎷夋牸鏈楁棩涔樻暟娉曪紝?f?x锛2(x?x0)+位?F?x锛0鈶?
绛旓細渚嬪Z锛漟(x,y),鍦▁oy骞抽潰涓婄殑鎶曞奖鏂圭▼. 浠=a,锛堝嵆浣滀笌XOY骞抽潰鐨勬埅闈,寰楁埅绾匡級寰梐=f(x,y),杩欏氨鏄埅绾垮湪XOY骞抽潰涓婄殑鎶曞奖鐨勬柟绋.鏁翠釜鏇查潰鐨鎶曞奖璁句负鐐归泦A,a鐨勫彇鍊奸泦鍚堣涓篗,鍒橝={锛坸,y)/f(x,y)=a,a灞炰簬A}
绛旓細鎵浠鏇查潰鍦ㄤ换鎰鐐(x,y,z)澶勭殑鍒囧钩闈㈢殑娉曞悜閲忔槸(2x,2y,-1).鍒囧钩闈笌 骞抽潰2x+4y-z=0骞宠,鎵浠2x/2=2y/4=(-1)/(-1),鎵浠=1,y=2.鎵浠=x^2+y^2=5,鍒囩偣鍧愭爣鏄(1,2,5).鍒囩墖鐨勬硶鍚戦噺鏄(2,4,-1).鎵姹傚垏骞抽潰鐨勬柟绋鏄2(x-1)+4(y-2)-(z-5)=0,鍗2x+4y-z-5=0.
绛旓細璁绌洪棿鏇查潰鈭鐨勬柟绋涓篎(x,y,z)=0锛岀偣M0(x0,y0,z0)鏄洸闈⑩垜涓婄殑涓鐐癸紝骞朵笖璁惧嚱鏁癋(x,y,z)鐨勫亸瀵兼暟鍦ㄧ偣M0杩炵画涓斾笉鍚屾椂涓洪浂銆傛洸闈⑩垜鐨勫弬鏁版柟绋媥=x(t),y=y(t),z=z(t) 鈫 F(x(t),y(t),z(t))鈮0 鈫 [F'xdx/dt+F'ydy/dt+F'zdz/dt]|t=t0 =0銆傛硶鍚戦噺n=F'x(x0,y0...
绛旓細鍏舵埅绾挎槸浜屾鏇茬嚎銆傞氬父锛屾垜浠皢涓夊厓浜屾鏂圭▼鎵琛ㄧず鐨鏇查潰绉颁綔浜屾鏇查潰銆傚钩闈㈠彨鍋氫竴娆℃洸闈備簩娆℃洸闈㈡槸鍦ㄤ笁缁村潗鏍囩郴(x銆亂銆亃)涓嬩笁鍏冧簩娆′唬鏁版柟绋嬪搴旂殑鎵鏈夊浘褰㈢殑缁熺О銆傚湪娆ф皬涓夌淮绌洪棿閲屽潗鏍噚,y,z涔嬮棿鐨勪簩娆℃柟绋嬶紙绯绘暟涓哄疄鏁帮紝涓斾簩娆￠」绯绘暟涓嶅叏涓洪浂锛夋墍琛ㄧず鐨勬洸闈傚笇鏈涙垜鑳藉府鍔╀綘瑙ｇ枒閲婃儜銆
绛旓細璁炬洸闈㈡柟绋涓 F锛圶锛孻锛孼锛夈傚叾瀵筙 Y Z鐨勫亸瀵煎垎鍒负 Fx锛圶锛孻锛孼锛夛紝Fy锛圶锛孻锛孼锛 锛孎z锛圶锛孻锛孼锛夈傚皢鐐癸紙a锛宐锛宑锛変唬鍏ュ緱 n锛濓蓟Fx锛孎y锛孎z锛 锛堝垏骞抽潰娉曞悜閲忥級銆傚啀灏嗗垏鐐癸紙a锛宐锛宑锛変唬鍏ュ緱銆傚垏骞抽潰鏂圭▼Fx锛婏紙X锛峚锛夛紜Fy锛婏紙Y锛峛锛夛紜Fz锛圸锛峜锛夛紳0銆傦紙姹傚垏骞抽潰鏂圭▼鐨...
绛旓細鍗宠В寰垎鏂圭▼锛-xy'+y=yy'+x y'=(y-x)/(x+y)浠=xu, 鍒檡'=u+xu'浠ｅ叆涓婂紡寰楋細u+xu'=(u-1)/(u+1)xu'=-(1+u^2)/(u+1)du(u+1)/(1+u^2)=-dx/x udu/(1+u^2)+du/(1+u^2)=-dx/x 0.5d(u^2)/(1+u^2)+du/(1+u^2)=-dx/x 绉垎锛0.5ln(1+u^2...
