2022年新人教版高中数学必修4知识点总结 .pdf

_ 精品资料高中数学必修 4 知识点总结第一章：三角函数1.1.1、任意角1、正角、负角、零角、象限角的概念.2、与角终边相同的角的集合：Zkk,2.1.1.2、弧度制1、把长度等于半径长的弧所对的圆心角叫做1 弧度的角.2、rl.3、弧长公式：RRnl180.4、扇形面积公式：lRRnS213602.1.2.1、任意角的三角函数1、设是一个任意角，它的终边与单位圆交于点yxP,，那么：xyxytan,cos,sin2、设点,A xy为角终边上任意一点，那么：（设22rxy）sinyr，cosxr，tanyx，cotxy3、sin，cos，tan在四个象限的符号和三角函数线的画法.正弦线：MP;余弦线：OM;正切线：AT4、特殊角 0，30，45，60，90，180，270 等的三角函数值.0 64322334322sincostan1.2.2、同角三角函数的基本关系式1、平方关系：1cossin22.2、商数关系：cossintan.3、倒数关系：tancot11.3、三角函数的诱导公式（概括为“奇变偶不变，符号看象限”Zk）TMAOPxy_ 精品资料1、诱导公式一：.tan2tan,cos2cos,sin2sinkkk（其中：Zk）2、诱导公式二：.tantan,coscos,sinsin3、诱导公式三：.tantan,coscos,sinsin4、诱导公式四：.tantan,coscos,sinsin5、诱导公式五：.sin2cos,cos2sin6、诱导公式六：.sin2cos,cos2sin1.4.1、正弦、余弦函数的图象和性质1、记住正弦、余弦函数图象：2、能够对照图象讲出正弦、余弦函数的相关性质：定义域、值域、最大最小值、对称轴、对称中心、奇偶性、单调性、周期性.3、会用五点法作图.sinyx在0,2 x上的五个关键点为：30 010-1 2022（，）（，）（，）（，）（，）.1.4.3、正切函数的图象与性质1、记住正切函数的图象：1-1y=cosx-32-52-727252322-2-4-3-2432-oyx1-1y=sinx-32-52-727252322-2-4-3-2432-oyx文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5_ 精品资料y=tanx322-32-2oyx2、记住余切函数的图象：y=cotx3222-2oyx3、能够对照图象讲出正切函数的相关性质：定义域、值域、对称中心、奇偶性、单调性、周期性.周期函数定义：对于函数xf，如果存在一个非零常数T，使得当x取定义域内的每一个值时，都有xfTxf，那么函数xf就叫做周期函数，非零常数T 叫做这个函数的周期.文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5_ 精品资料图表归纳：正弦、余弦、正切函数的图像及其性质xysinxycosxytan图象定义域RR,2|Zkkxx值域-1,1-1,1 R最值maxmin2,122,12xkkZyxkkZy时，时，maxmin2,12,1xkkZyxkkZy时，时，无周期性2T2TT奇偶性奇偶奇单调性Zk在2,222kk上单调递增在32,222kk上单调递减在2,2kk上单调递增在2,2kk上单调递减在(,)22kk上 单 调 递增对称性Zk对称轴方程：2xk对称中心(,0)k对称轴方程：xk对称中心(,0)2k无对称轴对称中心,0)(2k1.5、函数xAysin的图象1、对于函数：sin0,0yAxB A有：振幅 A，周期2T，初相，相位x，频率21Tf.2、能够讲出函数xysin的图象与sinyAxB的图象之间的平移伸缩变换关系.先平移后伸缩：sinyx平移|个单位sinyx（左加右减）横坐标不变sinyAx纵坐标变为原来的A倍纵坐标不变sinyAx文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5_ 精品资料横坐标变为原来的1|倍平移|B个单位sinyAxB（上加下减）先伸缩后平移：sinyx横坐标不变sinyAx纵坐标变为原来的A倍纵坐标不变sinyAx横坐标变为原来的1|倍平移个单位sinyAx（左加右减）平移|B个单位sinyAxB（上加下减）3、三角函数的周期，对称轴和对称中心函数sin()yx，xR及函数cos()yx，xR(A,为常数，且A0)的周期2|T；函数tan()yx，,2xkkZ(A,为常数，且A 0)的周期|T.对于sin()yAx和cos()yAx来说，对称中心与零点相联系，对称轴与最值点联系.求函数sin()yAx图像的对称轴与对称中心，只需令()2xkkZ与()xkkZ解出x即可.余弦函数可与正弦函数类比可得.4、由图像确定三角函数的解析式利用图像特征：maxmin2yyA，maxmin2yyB.要根据周期来求,要用图像的关键点来求.1.6、三角函数模型的简单应用1、要求熟悉课本例题.第三章、三角恒等变换3.1.1、两角差的余弦公式记住 15的三角函数值：sincostan12426426323.1.2、两角和与差的正弦、余弦、正切公式1、sincoscossinsin文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5_ 精品资料2、sincoscossinsin3、sinsincoscoscos4、sinsincoscoscos5、tantan1 tantantan.6、tantan1 tantantan.3.1.3、二倍角的正弦、余弦、正切公式1、cossin22sin，变形：12sincossin2.2、22sincos2cos1cos222sin21.变形如下：升幂公式：221cos22cos1cos22sin降幂公式：221cos(1cos2)21sin(1 cos2)23、2tan1tan22tan.4、sin 21cos2tan1cos2sin 23.2、简单的三角恒等变换1、注意正切化弦、平方降次.2、辅助角公式)sin(cossin22xbaxbxay（其中辅助角所在象限由点(,)a b的象限决定,tanba).第二章：平面向量2.1.1、向量的物理背景与概念1、了解四种常见向量：力、位移、速度、加速度.2、既有大小又有方向的量叫做向量.2.1.2、向量的几何表示1、带有方向的线段叫做有向线段，有向线段包含三个要素：起点、方向、长度.2、向量AB的大小，也就是向量AB的长度（或称模），记作ABuuu r；长度为零的向量叫做零向量；长度等于 1个单位的向量叫做单位向量.3、方向相同或相反的非零向量叫做平行向量（或共线向量）.规定：零向量与任意向量平行.文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5文档编码:CO6L2T2T2M9 HB6L2M7O1V4 ZG5P4I10T6E5