曲面上一个点能有几个切平面？ 求不在曲面上的点的切平面方程
\u8fc7\u66f2\u9762\u5916\u4e24\u70b9\u505a\u66f2\u9762\u7684\u5207\u5e73\u9762\u53ef\u4ee5\u505a\u51e0\u4e2a\uff1f\u4e09\u70b9\u4e00\u9762\uff0c\u7b2c\u4e09\u70b9\u5728\u66f2\u9762\u4e0a\u53d6\uff0c\u8be5\u5e97\u4e0e\u66f2\u9762\u7403\u5fc3\u8fde\u7ebf\u9700\u540c\u65f6\u5782\u76f4\u4e8e\u8be5\u70b9\u4e0e\u66f2\u9762\u5916\u4e24\u70b9\u7684\u8fde\u7ebf\u3002
\u5f53\u7403\u5fc3\u4e0e\u66f2\u9762\u5916\u4e24\u70b9\u4e0d\u5728\u540c\u4e00\u76f4\u7ebf\u4e0a\u65f6\uff0c\u7b2c\u4e09\u70b9\u53ef\u53d6\u4f4d\u7f6e\u6709\u4e24\u4e2a\u3002
\u59d0\u773c\u795e\u4e0d\u592a\u597d\uff0c\u4f60\u7ad6\u7740\u56fe\u7247\u4e0d\u662f\u5728\u96be\u4e3a\u6211\u4e48\uff01\u8f7b\u677e\u4e00\u4e0b\u54e6\u3002
F(x\uff0cy\uff0cz) \uff1d 3x² + 3y² + z² - 16
Fx (-1\uff0c-2\uff0c+3) = 6x | \u5728\u70b9\u5904\u7684\u504f\u5bfc\u6570 \uff1d - 6
Fy (-1\uff0c-2\uff0c+3)= 6y \uff1d -12
Fz (-1\uff0c-2\uff0c+3) \uff1d2z \uff1d +6
\u56e0\u6b64\u6240\u6c42\u5207\u5e73\u9762\u65b9\u7a0b\u4e3a\uff1a
(- 6) *[x - (-1)] + (-12) * [y - (-2)] + (+6) * [z - 3] = 0
\u6574\u7406\u5f97\uff1a x + 2y - z + 8 \uff1d 0
\u6240\u6c42\u6cd5\u7ebf\u65b9\u7a0b\u4e3a\uff1a (x +1)\uff0f(-6) \uff1d (y + 2)\uff0f(-12) \uff1d (z - 3)\uff0f\uff08+6\uff09
\u5373 (x +1)\uff0f1 \uff1d (y + 2)\uff0f2 \uff1d (z - 3)\uff0f\uff08-1\uff09
\u6ce8\u91ca\uff1a
\u82e5\u628a\u504f\u5bfc\u6570\uff08\u66f2\u9762\u5728\u70b9P\u5904\u7684\u6cd5\u5411\u91cf\uff09\u8bb0\u4f5c\uff1a - 6*\uff081\uff0c 2\uff0c -1\uff09
\u5219\u4ee5\u4e0a\u6b65\u9aa4\u53ef\u4ee5\u66f4\u4e3a\u7b80\u5316\uff1a
\u6cd5\u5e73\u9762\u65b9\u7a0b\u4e3a\u3014\u6cd5\u76f8\u91cf\u3015 \u70b9\u4e58 \u3014\u5e73\u9762\u4e0a\u70b9\u5230P\u7684\u5411\u91cf\u3015 \uff1a
-6* \u30141\uff0c2\uff0c-1\u3015 \u00b7 \u3014x-(-1)\uff0c y-(-2)\uff0c z - 3 \u3015 \uff1d 0
绛旓細娉曞悜閲弉=(Fx,Fy,Fz)=(1/2鈭歺,1/2鈭歽,1/2鈭歾)鍒欎换鎰忎竴鐐,璁句负(x0,y0,z0)鐨鍒囧钩闈涓1/2鈭歺0(x-x0)+1/2鈭歽0(y-y0)+,1/2鈭歾0(z-z0)=0鎴窛鍒嗗埆涓,鈭歛*鈭歺0,鈭歛*鈭歽0,鈭歛*鈭歾0鈭歛*鈭歺0+鈭歛*鈭歽0+鈭歛*鈭歾0=鈭歛*(鈭歺0+鈭歽0+鈭歾0)=鈭歛*鈭歛=a璇佹瘯.
绛旓細浠(x,y,z)=鈭歺+鈭歽+鈭歾-鈭歛锛屽湪鏇查潰涓浠诲彇涓鐐(x0,y0,z0)锛屽垯杩囪鐐圭殑鍒囧钩闈涓篎'x(x-x0)+F'y(y-y0)+F'z(z-z0)=0锛屾眰鍑鸿鐐圭殑鍚勫亸瀵兼暟F'x=1/2鈭歺0锛孎'y=1/2鈭歽0锛孎'z=1/2鈭歾0锛屾晠鍒囧钩闈㈡柟绋嬩负 (x-x0)/鈭歺0+(y-y0)/鈭歽0+(z-z0)/鈭歾0=0锛屼护y=z=...
绛旓細F(x,y,z)=e^z-z^2+xy-2=0;F'x=y(娉:姝ゅ涓篎瀵箈姹傚亸瀵煎緱鍒皔锛屽悗鍚岀悊)锛汧'y=x锛汧'z=e^z-2路z锛涘皢鍒囩偣(1,1,0)甯﹀叆涓婂紡寰楋細F'x=1锛汧'y=1锛汧'z=1鍗充负璇ュ钩闈㈢殑娉曞悜閲忥紝鍦ㄧ粨鍚堝垏鐐瑰潗鏍囷紝濂楃敤骞抽潰鐨勨滅偣娉曞紡鈥濓紝鍒欐墍姹鍒囧钩闈鏂圭▼涓 1路(x-1)+1路(y-1) 1路(z-0...
绛旓細鍦鏇查潰涓姹備竴鐐,浣胯鐐圭殑鍒囧钩闈骞宠浜庡彟涓骞抽潰,鍏蜂綋棰樼洰鐪嬪浘銆傛眰瑙ｏ綖 鎴戞潵绛 1涓鍥炵瓟 #娲诲姩# 鍙備笌閫犲彞澶ф寫鎴,绛旈鐡滃垎涓囧厓璞ぜ 瑗垮煙鐗涗粩鐜4672747 2017-06-15 路 鐭ラ亾鍚堜紮浜烘暀鑲茶瀹 瑗垮煙鐗涗粩鐜4672747 鐭ラ亾鍚堜紮浜烘暀鑲茶瀹 閲囩撼鏁:29975 鑾疯禐鏁:142397 姣曚笟浜庢渤鍗楀笀鑼冨ぇ瀛﹁绠楁暟瀛︿笓涓,瀛﹀＋瀛︿綅, ...
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绛旓細绛旀鏄疍銆傝F(x,y,z)=z-x-f(y-z)锛屽垯鏇查潰涓浠讳竴鐐瑰鐨鍒囧钩闈鐨勬硶鍚戦噺鏄(Fx,Fy,Fz)=(-1,-f',1+f')銆傛帴涓嬫潵鎵涓涓甯稿悜閲忎笌娉曞悜閲忓钩琛屾垨鍨傜洿锛岀壍娑夊埌f'锛屽钩琛岀殑甯稿悜閲忔壘涓嶅埌锛岃甯稿悜閲(A,B,C)涓庢硶鍚戦噺鍨傜洿锛屽垯-A-Bf'+C(1+f')=(-A+C)+(C-B)f'=0锛屽彧瑕佽-A+C=0,...
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绛旓細灏嗘柟绋嬫暣鐞嗕负鎴窛寮,寰楋細x/锛堚垰x0*锛堚垰x0+鈭歽0+鈭歾0))+y/(鈭歽0*(鈭歺0+鈭歽0+鈭歾0))+z/(鈭歾0*(鈭歺0+鈭歽0+鈭歾0))=1 鍥犱负锛坸0,y0,z0)鍦鏇查潰鈭歺+鈭歽+鈭歾=鈭歛涓 鎵浠ユ湁鈭歺0+鈭歽0+鈭歾0=鈭歛 鍒囬潰鏂圭▼鍙寲涓猴細x/(鈭歛x0)+y/(鈭歛y0)+z/(鈭歛z0)=1 3涓埅璺濅箣鍜屼负锛...
绛旓細*(1,2,1)锛1锛4a锛3a^2锛0锛屽緱a锛-1鎴-1/3锛屾墍浠ョ偣P鐨勫潗鏍囨槸(-1,1,-1)鎴(-1/3,1/9,-1/27)鎵浠ワ紝鏇茬嚎涓婄偣(-1,1,-1)鎴(-1/3,1/9,-1/27)澶勭殑鍒囩嚎骞宠浜庡钩闈+2y+z锛4 2銆佽鏇查潰涓婄偣P(a,b,c)澶勭殑鍒囧钩闈骞宠浜庡钩闈+4y+6z锛0锛屽垯鍒囧钩闈㈢殑娉曞悜閲忓钩琛屼簬(1,...
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