2022年平面向量的实际背景及基本概念习题 .pdf

ABCEDFO平面向量的实际背景及基本概念练习题一、选择题：1下列物理量中，不能称为向量的是（）A质量B速度C位移D力2设O是正方形ABCD的中心，向量AO、OB、CO、OD 是（）A平行向量B有相同终点的向量C相等向量D模相等的向量3下列命题中，正确的是（）A|ababB|ababC aba 与 b共线D|00aa4在下列说法中，正确的是（）A两个有公共起点且共线的向量，其终点必相同B模为 0 的向量与任一非零向量平行C向量就是有向线段D若|ab，则 ab5下列各说法中，其中错误的个数为（）（1）向量 AB 的长度与向量BA 的长度相等；（2）两个非零向量a 与 b 平行，则 a 与 b的方向相同或相反；（3）两个有公共终点的向量一定是共线向量；（4）共线向量是可以移动到同一条直线上的向量；（5）平行向量就是向量所在直线平行A2 个B3 个C4 个D5 个*6ABC中，D、E、F分别为BC、CA、AB的中点，在以A、B、C、D、E、F为端点的有向线段所表示的向量中，与EF 共线的向量有（）A2 个B3 个C6 个D7 个二、填空题：7在（1）平行向量一定相等；（2）不相等的向量一定不平行；（3）共线向量一定相等；（4）相等向量一定共线；（5）长度相等的向量是相等向量；（6）平行于同一个向量的两个向量是共线向量中，说法错误的是8如图，O是正方形ABCD的对角线的交点，四边形OAED、OCFB是正方形，在图中所示的向量中，（1）与 AO 相等的向量有；（2）与 AO 共线的向量有；（3）与 AO 模相等的向量有；（4）向量 AO 与 CO 是否相等？答：9O是正六边形ABCDEF的中心，且AOa，OBb，ABc，在以A、B、C、D、E、F、O为端点的向量中：（1）与 a 相等的向量有；（2）与 b 相等的向量有；OABCDEFABPabcde（3）与 c 相等的向量有*10下列说法中正确是（写序号）（1）若 a 与 b是平行向量，则a与 b 方向相同或相反；（2）若 AB 与 CD 共线，则点A、B、C、D共线；（3）四边形ABCD为平行四边形，则AB=CD；（4）若 ab，bc，则 ac；（5）四边形ABCD中，ABDC 且|ABAD，则四边形ABCD为正方形；（6）a与 b 方向相同且|ab 与 ab 是一致的；三、解答题：11如图，以 1 3 方格纸中两个不同的格点为起点和终点的所有向量中，有多少种大小不同的模？有多少种不同的方向？12在如图所示的向量a、b、c、d、e中（小正方形边长为1）是否存在共线向量？相等向量？模相等的向量？若存在，请一一举出13 某人从A点出发向西走了200m 达到B点，然后改变方向向西偏北60 走了 450m 到达C点，最后又改变方向向东走了200m 到达D点（1）作出向量AB、BC、CD（1cm 表示 200m）；（2）求 DA 的模*14如图，中国象棋的半个棋盘上有一只“马”，开始下棋时它位于A点，这只“马”第一步有几种可能的走法？试在图中画出来；若它位于图中的P点，则这只“马”第一步有几种可能的走法？它能否走若干步从A点走到与它相邻的B点处？文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7FEDCBABADCO 2.2.1 向量加减运算一、选择题：1化简 PMPNMN 所得的结果是（）A MPB NPC 0D MN2设 OAa，OBb 且|6ab，120AOB，则|ab 等于（）A36 B12 C6 D 6 33 a，b 为非零向量，且|abab，则（）A a 与 b方向相同B abC abD a 与 b 方向相反4在平行四边形ABCD中，若|BCBABCAB，则必有（）AABCD为菱形BABCD为矩形CABCD为正方形D以上皆错5已知正方形ABCD边长为 1，ABa，BCb，ACc，则|abc 等于（）A0 B3 C 2 2D2*6设()()ABCDBCDAa，而 b 是一非零向量，则下列个结论：（1）a 与 b 共线；（2）aba；（3）abb；（4）|abab 中正确的是（）A（1）（2）B（3）（4）C（2）（4）D（1）（3）二、填空题：7在平行四边形ABCD中，ABa，ADb，则 CA，BD8在 a“向北走 20km”，b“向西走 20km”，则 ab 表示9若|8AB，|5AC，则|BC 的取值范围为*10一艘船从A点出发以 2 3 km/h 的速度向垂直于河岸的方向行驶，而船实际行驶速度的大小为 4km/h，则河水的流速的大小为三、解答题：11如图，O是平行四边形ABCD外一点，用 OA、OB、OC 表示 OD 12 如图，在任意四边形ABCD中，E、F分别为AD、BC的中点，求证：ABDCEFEF 文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O713飞机从甲地按南偏东10 方向飞行2000km 到达乙地，再从乙地按北偏西70 方向飞行2000km 到达丙地，那么丙地在甲地的什么方向？丙地距离甲地多远？*14点D、E、F分别是ABC三边AB、BC、CA上的中点，求证：（1）ABBEACCE；（2）0EAFBDCC A B F E D 文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 ZH2Y1O4B10O7文档编码:CZ4R10G10P10S5 HF5I3O5Q8H2 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