1、1,2,1s1 2,1,1s2|s|s|/sscos2121 21.3 ),1,2,4()2,3,1(),1,2,4()10,1,2()1,2,2(00yxn 11222200 yx.2,1000 zyx3,2,1200tt 103410n0200 ttt310 t22yxyxf 22yxxyf .igrad)1,0(f)1,1,1(n.2 zyx.4c)ba(2)ac()cb()ba(.22516946 d.1,1,1n .043 zyx.1,3,11,1,21,0,1n .023 zyx2,1,4n 2,3,6n .3,2,2n .3,2,051.1222yzx .2,2,192.2.33
2、.32411341354141414)6(lu.1.0,02 ayxazayax0)1()1(:1 zCByxA,0,02 CBACBA.0123 zyx ,0123,012zyxzyx ).1(21,2yzyx2222)1(414 yyzxL0)2(72 yxzx 0722)1(zyx ),(000zyx【解解】过直线过直线的平面束方程为的平面束方程为即即 设切点为设切点为 0722)1(213232221000202020000zyxzyxzyx )2,0,3(:,32,0M )2,0,3(72 zx)2,2,1(2164 zyx则则点点处切平面处切平面；点；点处切平面处切平面.或或(1,
3、2,2)(1,2,2)2,3,1()2,1,1()1,1,1(21 nn 032012zyxzyx【解解】过直线过直线的平面束方程为的平面束方程为0)32(12 zyxzyx 031)21()2()1(zyx即即 0)21(2)2(3)1(25 .0171293 zyx j)2(i)2(),(grad0000),(00yxxyyxhyx .855)2()2(),(00202020020000yxyxyxxyyxg )75(855),(2222xyyxxyyxyxL ，),(),(2yxgyxf .075,0)2(8100)2(81022xyyxLxyxyLxyyxLxyx ),5,5(),5,5(21 MM).35,35(),35,35(43 MM450)()(21 MfMf.150)()(41 MfMfjyzixzgradz 361619,361614,/,2222yxyyxxyzxzdydx,94ydyxdx 94Cxy 3,1 yx3 C)11,3,1(P 94223361614xyyxz
