新高考数学一轮复习讲与练第09讲 平面向量（练）（原卷版）

第01讲平面向量1．已知四边形SKIPIF1<0是矩形，SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．若平面向量SKIPIF1<0两两的夹角相等，且SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<03．已知非零向量SKIPIF1<0、SKIPIF1<0满足SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．在SKIPIF1<0中，点SKIPIF1<0在SKIPIF1<0边上，SKIPIF1<0．记SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．若非零向量SKIPIF1<0，SKIPIF1<0满足SKIPIF1<0，SKIPIF1<0，则向量SKIPIF1<0与SKIPIF1<0的夹角为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知向量SKIPIF1<0且SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知向量SKIPIF1<0，SKIPIF1<0满足SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0_____________.8．已知平面向量SKIPIF1<0，SKIPIF1<0，SKIPIF1<0满足SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0的值为________.9．已知向量SKIPIF1<0满足SKIPIF1<0,SKIPIF1<0，SKIPIF1<0与SKIPIF1<0的夹角为SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0_______．10．已知平面向量SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0.(1)求向量SKIPIF1<0与SKIPIF1<0的夹角；(2)当k为何值时，向量SKIPIF1<0与SKIPIF1<0垂直？11．已知向量SKIPIF1<0满足SKIPIF1<0．(1)求SKIPIF1<0的值；(2)求SKIPIF1<0的值．1．已知向量SKIPIF1<0满足SKIPIF1<0，则向量SKIPIF1<0与SKIPIF1<0夹角的最大值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．SKIPIF1<0中，若SKIPIF1<0，则SKIPIF1<0的值为（

）A．2 B．4 C．SKIPIF1<0 D．SKIPIF1<03．在等腰梯形SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0分别为SKIPIF1<0的中点，SKIPIF1<0为SKIPIF1<0的中点，则SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．在SKIPIF1<0中，已知SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0为（）A．等边三角形B．直角三角形C．等腰三角形D．三边均不相等的三角形5．已知向量SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0的值为（

）A．5 B．10 C．15 D．206．设SKIPIF1<0，SKIPIF1<0，SKIPIF1<0为平面内任意三点，则“SKIPIF1<0与SKIPIF1<0的夹角为钝角”是“SKIPIF1<0”的（

）A．必要不充分条件 B．充分不必要条件C．充要条件 D．既不充分也不必要条件7．已知任意平面向量SKIPIF1<0，把SKIPIF1<0绕其起点沿逆时针方向旋转SKIPIF1<0角得到向量SKIPIF1<0，叫做把点SKIPIF1<0绕点SKIPIF1<0沿逆时针方向旋转SKIPIF1<0角得到点SKIPIF1<0.已知平面内点SKIPIF1<0，点SKIPIF1<0，把点SKIPIF1<0绕点SKIPIF1<0沿逆时针方向旋转SKIPIF1<0得到点SKIPIF1<0，则向量SKIPIF1<0在向量SKIPIF1<0上的投影向量为___________.（用坐标作答）8．已知SKIPIF1<0是抛物线SKIPIF1<0上的点，F是抛物线C的焦点，若SKIPIF1<0，则SKIPIF1<0______．9．已知SKIPIF1<0为SKIPIF1<0内一点，且满足SKIPIF1<0，则SKIPIF1<0为SKIPIF1<0的________心．10．如图，在平行四边形SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，E为边SKIPIF1<0的中点，SKIPIF1<0，若SKIPIF1<0，则SKIPIF1<0______.三、解答题11．如图所示，在SKIPIF1<0中，SKIPIF1<0与SKIPIF1<0相交于点SKIPIF1<0.(1)用SKIPIF1<0和SKIPIF1<0分别表示SKIPIF1<0和SKIPIF1<0；(2)若SKIPIF1<0，求实数SKIPIF1<0和SKIPIF1<0的值.12．已知SKIPIF1<0，SKIPIF1<0是SKIPIF1<0的中点(1)若SKIPIF1<0，求向量SKIPIF1<0与向量SKIPIF1<0的夹角的余弦值；(2)若SKIPIF1<0是线段SKIPIF1<0上的任意一点，且SKIPIF1<0，求SKIPIF1<0的最小值．1．（2022年全国新高考II卷数学试题）已知向量SKIPIF1<0，若SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．5 D．62．（2022年全国高考乙卷数学（文）试题）已知向量SKIPIF1<0，则SKIPIF1<0（

）A．2 B．3 C．4 D．53．（2022年北京市高考数学试题）在SKIPIF1<0中，SKIPIF1<0．P为SKIPIF1<0所在平面内的动点，且SKIPIF1<0，则SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022年全国高考乙卷数学（理）试题）已知向量SKIPIF1<0满足SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．25．（2022年全国新高考II卷数学试题）已知O为坐标原点，过抛物线SKIPIF1<0焦点F的直线与C交于A，B两点，其中A在第一象限，点SKIPIF1<0，若SKIPIF1<0，则（

）A．直线SKIPIF1<0的斜