新高考數(shù)學(xué)一輪復(fù)習(xí)分層提升練習(xí)第24練 平面向量的數(shù)量積及其應(yīng)用（原卷版）

第24練平面向量的數(shù)量積及其應(yīng)用（精練）刷真題明導(dǎo)向刷真題明導(dǎo)向一、單選題1．）已知向量SKIPIF1<0，則SKIPIF1<0（

）A．2 B．3 C．4 D．52．已知向量SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知向量SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．24．已知向量SKIPIF1<0，若SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．已知向量SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．5 D．66．已知向量SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．0 D．17．已知非零向量SKIPIF1<0，則“SKIPIF1<0”是“SKIPIF1<0”的（

）A．充分不必要條件 B．必要不充分條件C．充分必要條件 D．既不充分又不必要條件8．已知向量SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．在SKIPIF1<0中，SKIPIF1<0．P為SKIPIF1<0所在平面內(nèi)的動(dòng)點(diǎn)，且SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空題10．已知向量SKIPIF1<0．若SKIPIF1<0，則SKIPIF1<0______________．11．已知向量SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0__________．12．已知向量SKIPIF1<0．若SKIPIF1<0，則SKIPIF1<0________．13．若向量SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0_________.14．設(shè)向量SKIPIF1<0，SKIPIF1<0的夾角的余弦值為SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0_________．15．已知向量SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0______．16．已知向量SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0_______．三、雙空題17．在邊長(zhǎng)為1的等邊三角形ABC中，D為線段BC上的動(dòng)點(diǎn)，SKIPIF1<0且交AB于點(diǎn)E．SKIPIF1<0且交AC于點(diǎn)F,則SKIPIF1<0的值為____________；SKIPIF1<0的最小值為____________．【A組】一、單選題1．已知向量SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．5 C．SKIPIF1<0 D．102．）設(shè)SKIPIF1<0都是單位向量，且SKIPIF1<0，則向量SKIPIF1<0的夾角等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知向量SKIPIF1<0在向量SKIPIF1<0上的投影向量是SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．如圖，已知SKIPIF1<0的半徑為2，SKIPIF1<0，則SKIPIF1<0（

）

A．1 B．-2 C．2 D．SKIPIF1<05．已知向量SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．56．已知平面向量SKIPIF1<0與SKIPIF1<0的夾角是SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知向量SKIPIF1<0，SKIPIF1<0與SKIPIF1<0共線，則SKIPIF1<0=（

）A．6 B．20 C．SKIPIF1<0 D．58．已知單位向量SKIPIF1<0滿足SKIPIF1<0，其中SKIPIF1<0，則SKIPIF1<0在SKIPIF1<0上的投影向量是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則向量SKIPIF1<0在向量SKIPIF1<0方向上的投影向量為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知向量SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0與SKIPIF1<0夾角的余弦值為SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．12 D．7211．在△ABC中，SKIPIF1<0，SKIPIF1<0且點(diǎn)D滿足SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．已知向量SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．12 D．2413．已知向量SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則實(shí)數(shù)m的值為（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．114．若平面向量SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0與SKIPIF1<0垂直，則SKIPIF1<0與SKIPIF1<0的夾角為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．平行四邊形SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．4 D．816．在矩形SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為SKIPIF1<0邊的中點(diǎn)，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<017．已知向量SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的最小值為（）A．7 B．SKIPIF1<0C．7＋4SKIPIF1<0 D．4SKIPIF1<0二、多選題18．）已知平面向量SKIPIF1<0，SKIPIF1<0，則下列說法正確的是（

）A．SKIPIF1<0B．SKIPIF1<0在SKIPIF1<0方向上的投影向量為SKIPIF1<0C．與SKIPIF1<0垂直的單位向量的坐標(biāo)為SKIPIF1<0D．若向量SKIPIF1<0與非零向量SKIPIF1<0共線，則SKIPIF1<019．已知向量SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0在SKIPIF1<0上的投影向量是SKIPIF1<020．已知向量SKIPIF1<0，SKIPIF1<0//SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<021．已知向量SKIPIF1<0，SKIPIF1<0，則下列說法正確的是（

）A．若SKIPIF1<0，則SKIPIF1<0 B．若SKIPIF1<0∥SKIPIF1<0，則SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0 D．若SKIPIF1<0，則向量SKIPIF1<0，SKIPIF1<0的夾角為鈍角22．已知向量SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<023．有關(guān)平面向量的說法，下列錯(cuò)誤的是（

）A．若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0 B．若SKIPIF1<0與SKIPIF1<0共線且模長(zhǎng)相等，則SKIPIF1<0C．若SKIPIF1<0且SKIPIF1<0與SKIPIF1<0方向相同，則SKIPIF1<0 D．SKIPIF1<0恒成立三、填空題24．已知向量SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0___________.25．已知向量SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0___________.26．若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0______．27．已知向量SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0______28．已知單位向量SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0__________．29．已知非零向量SKIPIF1<0，SKIPIF1<0的夾角為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0______．30．已知向量SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0在SKIPIF1<0上的投影向量SKIPIF1<0______.31．已知菱形SKIPIF1<0中，SKIPIF1<0，則SKIPIF1<0__________.32．若平面四邊形SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，則該四邊形一定是______.33．在平行四邊形SKIPIF1<0中，若SKIPIF1<0，則SKIPIF1<0___________.【B組】一、單選題1．已知菱形SKIPIF1<0的邊長(zhǎng)為2，且SKIPIF1<0，則SKIPIF1<0的值為（

）A．2 B．4 C．6 D．82．若向量SKIPIF1<0、SKIPIF1<0滿足SKIPIF1<0，則向量SKIPIF1<0與向量SKIPIF1<0的夾角為（

）A．30° B．60° C．120° D．150°3．正SKIPIF1<0的邊長(zhǎng)為2，SKIPIF1<0，則SKIPIF1<0（

）A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．如圖所示，邊長(zhǎng)為2的正三角形ABC中，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．-1 B．-2 C．1 D．25．已知SKIPIF1<0，SKIPIF1<0為單位向量，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．SKIPIF1<0中，|SKIPIF1<0|=2|SKIPIF1<0|，則sinA的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．若SKIPIF1<0，SKIPIF1<0均為單位向量，且SKIPIF1<0，則k的值可能是（

）A．-2 B．2 C．3 D．-38．已知SKIPIF1<0，SKIPIF1<0是單位向量，且SKIPIF1<0，則向量SKIPIF1<0與SKIPIF1<0的夾角為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．點(diǎn)SKIPIF1<0是SKIPIF1<0的重心，SKIPIF1<0，則SKIPIF1<0（

）A．32 B．30 C．16 D．1410．已知平面向量SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．-1 B．0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題11．已知向量SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0在SKIPIF1<0上的投影向量是SKIPIF1<0 D．SKIPIF1<0在SKIPIF1<0上的投影向量是SKIPIF1<012．）設(shè)SKIPIF1<0，非零向量SKIPIF1<0，SKIPIF1<0，則（

）.A．若SKIPIF1<0，則SKIPIF1<0 B．若SKIPIF1<0，則SKIPIF1<0C．存在SKIPIF1<0，使SKIPIF1<0 D．若SKIPIF1<0，則SKIPIF1<013．已知向量SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．在△ABC中，點(diǎn)D，E分別是BC，AC的中點(diǎn)，點(diǎn)O為△ABC內(nèi)的一點(diǎn)，則下列結(jié)論正確的是（

）A．若SKIPIF1<0，則SKIPIF1<0B．若SKIPIF1<0，則SKIPIF1<0C．若SKIPIF1<0，則SKIPIF1<0D．若點(diǎn)O為△ABC的外心，BC＝4，則SKIPIF1<0三、填空題15．已知向量SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則向量SKIPIF1<0與SKIPIF1<0的夾角為______．16．在邊長(zhǎng)為6的正SKIPIF1<0中，若點(diǎn)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0__________.17．已知平面內(nèi)非零向量SKIPIF1<0，滿足SKIPIF1<0，則SKIPIF1<0__________.18．如圖，圓SKIPIF1<0為SKIPIF1<0的外接圓，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為邊SKIPIF1<0的中點(diǎn)，則SKIPIF1<0______.19．已知平面向量SKIPIF1<0滿足SKIPIF1<0且SKIPIF1<0，當(dāng)向量SKIPIF1<0與向量SKIPIF1<0的夾角最大時(shí)，向量SKIPIF1<0的模為______．20．已知平面向量SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值為_________21．已知向量SKIPIF1<0滿足SKIPIF1<0，對(duì)任意的SKIPIF1<0的最小值為SKIPIF1<0，則SKIPIF1<0與SKIPIF1<0的夾角為________．【C組】一、單選題1．在SKIPIF1<0中，設(shè)SKIPIF1<0，那么動(dòng)點(diǎn)SKIPIF1<0的軌跡必通過SKIPIF1<0的（

）A．垂心 B．內(nèi)心 C．外心 D．重心2．已知A，B，C是單位圓上的三個(gè)動(dòng)點(diǎn)，則SKIPIF1<0的最小值是（

）A．0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．圓SKIPIF1<0為銳角SKIPIF1<0的外接圓，SKIPIF1<0，點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知平面向量SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知平面向量SKIPIF1<0、SKIPIF1<0、SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0與SKIPIF1<0所成夾角的最大值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知SKIPIF1<0