求曲面x2+2y2+3z2=21在点(1,-2,2)处的切平面和法线方程 求曲面3x2+y2+z2=16在点(-1,-2,3)处的切平...
\u6c42\u66f2\u9762x²+2y²+3z²=21\u5728\u70b9(-1,-2,2)\u5904\u7684\u5207\u5e73\u9762\u4e0e\u6cd5\u7ebf\u65b9\u7a0b\u8bbef\uff08x,y,z\uff09=x²+2y²+3z²=21.\u5207\u5411\u91cf\uff1an\u5411\u91cf=\uff082x,4y,6z\uff09|\uff08-1\uff0c-2\uff0c2\uff09=\uff08-2\uff0c-8\uff0c12\uff09
\u2234\u5207\u5e73\u9762\u65b9\u7a0b\uff1a\uff08-2\uff09\uff08x+1\uff09+\uff08-8\uff09(y+2)+12(z-2)=0
\u6cd5\u7ebf\u65b9\u7a0b\uff1ax+1/-2=y+2/-8=z-2/12
\u5199\u6210F(x.y.z)=0\u7684\u5f62\u5f0f\uff0c\u7136\u540eF(x.y.z)\u5206\u522b\u5bf9x\uff0cy\uff0cz\u6c42\u504f\u5bfc\uff0c\u4ee3\u5165\uff08-1\uff0c-2\uff0c3\uff09\u4fbf\u662f\u5f97\u5230\u7684\u4e09\u4e2a\u6570\u4fbf\u662f\u66f2\u9762\u6cd5\u5411\u91cf\uff08\u6cd5\u7ebf\uff09\u7684\u4e09\u4e2a\u6570\uff0c\u5207\u5e73\u9762\u53ef\u4ee5\u7528a\uff08x+1\uff09+b\uff08y+2\uff09+c\uff08z-3\uff09=0\u7684\u516c\u5f0f\uff0c1\uff0c2\uff0c-3\u662f\u51cf\u53bb\uff08-1\uff0c-2\uff0c3\uff09\u5bf9\u5e94\u7684\u6570\u3002a\uff0cb\uff0cc\u662f\u6cd5\u5411\u91cf\u5bf9\u5e94\u7684\u4e09\u4e2a\u6570
F(x、y、z)=x²+2y²+3z²-21n=(Fx、Fy、Fz)=(2x、4y、6z)
n|(1、-2、2)=(2、-8、12)
切平面方程:
2(x-1)-8(y+2)+12(z-2)=0
2x-8y+12z-42=0
法线方程:
(x-1)/2=(y+2)/(-8)=(z-2)/12
法线方程:
(x-1)/1=(y+2)/(-4)=(z-1)/3
绛旓細姹傛洸闈^2+2y^2+3z^2=12鍦(1,-2,1)澶勭殑鍒囧钩闈㈠強娉曠嚎鏂圭▼. 鎴戞潵绛 棣栭〉 鐢ㄦ埛 璁よ瘉鐢ㄦ埛 瑙嗛浣滆 甯府鍥 璁よ瘉鍥㈤槦 鍚堜紮浜 浼佷笟 濯掍綋 鏀垮簻 鍏朵粬缁勭粐 鍟嗗煄 娉曞緥 鎵嬫満绛旈 鎴戠殑 姹傛洸闈^2+2y^2+3z^2=12鍦(1,-2,1)澶勭殑鍒囧钩闈㈠強娉曠嚎鏂圭▼. 鎴戞潵绛 1涓洖绛 #鍥藉簡蹇呯湅...
绛旓細銆愮瓟妗堛戯細
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