《高等数学竞赛资料》空间解几(竞赛辅导).ppt

文档介绍：空间解析几何与向量代数与同向的单位向量记为:a?| |aa???aoao(cos , cos , cos )? ???,a b??以为邻边的平行四边形的面积.??a b?,a b????a b??????? M SdS????????????MS??直线L 上的任意点直线L 的方向向量ML0MS?? 2 1 21 2( )M M S SdS S?????????????????? ???1 2,M M1 2,S S?????直线L ,L 上的点21直线L ,L , 10, 12a b a b? ???? ???????求以, 2a b a b? ??? ??????解a b??????cosa b??????20cos??1212 3cos20 5?? ?4sin5??所求三角形面积1( ) ( 2 )2a b a b? ???? ??????122a b b a? ?????? ??????132a b? ???? ??32a b? ??? ??3sin2a b?? ?????24A=b??a??设向量平面例2?,非零向量在?逆时针转过角?得向量,用, ,a b?? ???表示b??c??c??b??a??c?a b??? ??内c?.?作向量解,它与a b??? ???内,在平面b??垂直,c??| |b??cos?bo?| |b??sin?0( )a b??? ??| |b???(cos sin )| || |b a bba b? ?????? ???? ????a b??? ??,a b?? ??| | 2, ,3b a b?? ????? ???0| | | |limxa x b ax?? ??? ????设是非零向量,,求:例30(| | | |)(| | | |)lim(| | | |)xa x b a a x b ax a x b a?? ? ???? ??? ???????????? ????2 20| | | |lim(| | | |)xa x b ax a x b a?? ??? ??? ?????? ????0( ) ( )lim(| | | |)xa x b a x b a ax a x b a?? ???? ??? ??????????? ??? ????2 202 | |lim(| | | |)xx a b x bx a x b a???? ????? ????? ????202 | |lim| | | |xa b x ba x b a???? ????? ????? ????22| |a ba????????原式| || | cos ,| |a b a ba? ???? ??? ?????1?解3 12 4 3x y z? ?? ?2 132x tyz t? ??????? ??求两直线、之间的距离. 例41 2 1 21 2( )M M S SdS S?????????????????? ???1(3, 0, 1)M?2( 1, 3, 2)M?1(2, 4, 3)S????2(2, 0,1)S????1 2( 4, 3, 3)M M? ????????1 2S S? ???? ???(4, 4, 8)?76?1M2M解9 24 3 1x y z? ?? ??1L2L7 22 9 2x y z? ?? ??求公垂线的方程公垂线L 的方向向量1 2S S? ???? ???S???(4, 3,1) ( 2, 9, 2)?