最新高考数学二轮复习热点题型专题二十五平面向量的概念及其线性运算优秀名师资料.doc

2015高考数学二轮复习热点题型专题二十五 平面向量的概念及其线性运算专题二十五 平面向量的概念及其线性运算 【高频考点解读】 1.了解向量的实际背景( 2.理解平面向量的概念，理解两个向量相等的含义( 3.理解向量的几何表示( 4.掌握向量加法、减法的运算，并理解其几何意义( 5.掌握向量数乘的运算及其几何意义，理解两个向量共线的含义( 6.了解向量线性运算的性质及其几何意义( 【热点题型】 题型一 向量的有关概念 例1、设a为单位向量，?若a为平面内的某个向量，则a,|a|a;?若a与a平行，000则a,|a|a;?若a与a平行且|a|,1，则a,a.上述命题中，假命题的个数是( ) 000A(0 B(1 C(2 D(3 【提分秘籍】 1(向量与有向线段 向量常用有向线段表示，它们是两个不同概念，有向线段由起点、终点方向唯一确定，而向量是由大小和方向来确定的( 2(零向量和单位向量是两个特殊的向量(它们的模确定，但方向不确定，在解题时注意它们的特殊性(如若a?b、b?c则a?c是假命题，因为当b为零向量时，b与c为任意向量，两者不一定平行( 3(共线向量也叫平行向量，两向量所在的直线可以共线也可以平行( 4(相等向量一定是平行向量( 【举一反三】 下列说法中正确的是( ) A(只有方向相同或相反的向量是平行向量 B(零向量的长度为零 procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 200 Yuan, construction person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the job unit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punished 1~2 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerning administrative sanctions, should be brought to the company or the relevant Department. (2) personal injury accident occurred, the direct punishment 0.5-10,000 yuan, responsible for the direct responsibility for the C(长度相等的两个向量是相等向量 D(共线向量是在一条直线上的向量 【热点题型】 题型二 向量的线性运算 ?例2、D是?ABC的边BA上的中点，则向量CD等于( ) ????11A(,BC，BA B(,BC,BA 22????11C.BC,BA D.BC，BA 22【提分秘籍】 1(两个向量的和仍是一个向量( 2(利用三角形法则进行加法运算时，两向量要首尾相连，和向量由第一个向量的起点指向第二个向量的终点(可结合物理中位移的合成来认识);利用平行四边形法则进行加法运算时，两向量要有相同的起点(可结合物理中力的合成来认识() 3(当两个向量共线时，三角形法则仍适用，而平行四边形法则不适用( 4(利用三角形法则进行减法运算时，两个向量要有相同的起点，然后连接两向量的终点，并指向被减向量即为差向量( 5(实数和向量可以求积，但不能求和或求差( 6(λ,0或a,0?λa,0. 【举一反三】 -2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-98 2 GB50128-nical equipment installation engineering 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mecha-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 8 JB4730-0 of welding procedure qualification for steel pressure vessels 7 JB/4709200-2004 petrochemical JB/ T4708-procedure 6 SH352510,000 yuan, responsible for the direct responsibility for the-the direct punishment 0.5dministrative sanctions, should be brought to the company or the relevant Department. (2) personal injury accident occurred, ning ad 1~2 million. Direct responsibility for the accident and have the corresponding responsibility of leadership, such as concerit fined 300 yuan, the unit will charge a fine of 100 Yuan. 7.5.3 accident penalties (1) injuries fatalities directly punishejob unconstruction person in charge a fine of 50 Yuan. (8) no permit to work and the job in accordance with the provisions, on the uan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 200 Yuan, f 50 Ys cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine oion standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using ga2000 construction installation engineering construct-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-pment installation engineering construction and acceptance specification for 5 GB502752009 mechanical equi-1997 steel welded atmospheric pressure vessel 4 GB50231- 2 - ?????在?ABCD中，AB,a，AD,b，AN,3NC， M为BC的中点，则MN,________.(用a，b表示) 【热点题型】 题型三 共线向量定理 例3、设两个非零向量a与b不共线( ???(1)若AB,a，b，BC,2a，8b，CD,3(a,b)(求证:A，B，D三点共线; ，kb共线( (2)试确定实数k，使ka，b和a【提分秘籍】 procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-。