3.1.2空间向量的数量积运算[定.pdf
城阳二中高二数学lA O P m n lg 城阳二中高二数学导学方案课题：3.1.2 空间向量的数量积运算命题人：侯卫峰学习目标：（1）能运用向量的数量积判断向量的共线与垂直（2）能运用空间向量的数量积求两个向量所成的角（3）能运用烧烤架求空间和（差）向量的模.重点和难点：教学重点：空间向量数量积公式及其应用。教学难点：如何将立体几何问题等价转化为向量问题；在此基础上，通过向量运算解决立体几何问题。感知尝试：(1)空间向量的夹角：(2)空间向量的数量积：已知空间中任意两个向量a、b，则 a b空间向量的数量积的常用结论：(a)cosa、b；(b)a2；(c)ab(3)空间向量的数量积的运算律：(a)交换律 a b；(b)分配律 a(bc)热点共探：例1:如图:,POPA分别是平面的垂线、斜线,AO 是PA在平面内的射影,llOA,求证:lPA.例2:如图:,m n是平面内的两条相交直线,如果,lm ln,求证:l.例 3 已知四面体ABCD 中，ABCD，AC BD，G、H 分别是 ABC 和 ACD 的重心求证：(1)AD BC；(2)GH BD提炼总结：城阳二中高二数学课堂达标：1.已知 PA平面 ABC，垂足为A，90ABC，PA=AB=BC=6，则 PC=（）（A）63（B）6（C）12（D）14 2若向量且向量和垂直向量Rbanbam,(,、则)0（）Anm/BnmCnmnm也不垂直于不平行于,D以上三种情况都可能3设 A、B、C、D 是空间不共面的四点，且满足0,0,0ADACADABACAB则 BCD 是（）A钝角三角形B直角三角形C锐角三角形D不确定4.已知222,22abab，则=5.在空间四边形ABCD 中，求证：0AB CDAC DBADBC.课后作业：A 组1空间四边形OABC中，OBOC，3AO BAO C，则 cos 的值是（）A21B22C21D 02在棱长为1 的正方体ABCD A1B1C1D1中，M 和 N 分别为A1B1和 BB1的中点，那么直线AM 与CN 所成角的余弦值是（）A52B52C53D10103若向量,94,2kjibkjia，则这两个向量的位置关系是_。4已知向量,3,5krjibkjima若/ab则实数 m_，r_。5若(3)ab)57(ba，且(4)ab)57(ba，则 a与b的夹角为 _。B 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