高三数学一轮复习试题：平面向量的基本定理
<p>导读：高考，比的不是智商高低，比的是谁的耐心好，经过一轮、二轮、三轮复习的摧残还能有几个小伙伴说自己屹立不倒的?今天数学网小编末宝就给大家带来了高考数学一轮复习的同步练习，快来看看吧。</p><p></p><p></p><p><p class="MsoNormal">4.<span>已知向量</span><b><i>a</i></b><span>＝</span>(<span>－</span>1<span>，</span>2)<span>，</span><b><i>b</i></b><span>＝</span>(3<span>，</span><i>m</i>)<span>，</span><i>m</i>∈<b>R</b><span>，则</span>“<i>m</i><span>＝－</span>6”<span>是</span>“<b><i>a</i></b>∥(<b><i>a</i></b><span>＋</span><b><i>b</i></b>)”<span>的</span>(<span> </span>)</p><p class="MsoNormal">A.<span>充分必要条件</span>B.<span>充分不必要条件</span></p><p class="MsoNormal">C.<span>必要不充分条件</span>D.<span>既不充分也不必要条件</span></p><p class="MsoNormal"><span>解析 由题意得</span><b><i>a</i></b><span>＋</span><b><i>b</i></b><span>＝</span>(2<span>，</span>2<span>＋</span><i>m</i>)<span>，由</span><b><i>a</i></b>∥(<b><i>a</i></b><span>＋</span><b><i>b</i></b>)<span>，得－</span>1×(2<span>＋</span><i>m</i>)<span>＝</span>2×2<span>，所以</span><i>m</i><span>＝－</span>6<span>，则</span>“<i>m</i><span>＝－</span>6”<span>是</span>“<b><i>a</i></b>∥(<b><i>a</i></b><span>＋</span><b><i>b</i></b>)”<span>的充要条件，故选</span>A.</p><p class="MsoNormal"><span>答案 </span>A</p></p><p></p><p><p class="MsoNormal">7.<span>已知</span><b><i>a</i></b><span>＝</span>(<span>，</span>1)<span>，若将向量－</span>2<b><i>a</i></b><span>绕坐标原点逆时针旋转</span>120°<span>得到向量</span><b><i>b</i></b><span>，则</span><b><i>b</i></b><span>的坐标为</span>(<span> </span>)</p><p class="MsoNormal">A.(0<span>，</span>4)B.(2<span>，－</span>2)</p><p class="MsoNormal">C.(<span>－</span>2<span>，</span>2)D.(2<span>，－</span>2)</p><p class="MsoNormal"><span>解析 </span>∵<b><i>a</i></b><span>＝</span>(<span>，</span>1)<span>，</span>∴－2<b><i>a</i></b><span>＝</span>(<span>－</span>2<span>，－</span>2)<span>，易知向量－</span>2<b><i>a</i></b><span>与</span><i>x</i><span>轴正半轴的夹角</span><i>α</i><span>＝</span>150°(<span>如图</span>).<span>向量－</span>2<b><i>a</i></b><span>绕坐标原点逆时针旋转</span>120°<span>得到向量</span><b><i>b</i></b><span>，在第四象限，与</span><i>x</i><span>轴正半轴的夹角</span><i>β</i><span>＝</span>30°<span>，</span>∴<b><i>b</i></b><span>＝</span>(2<span>，－</span>2)<span>，故选</span>B.</p><p class="MsoNormal"></p><p class="MsoNormal">12.<span>如图，在平行四边形</span><i>ABCD</i><span>中，</span><i>M</i><span>，</span><i>N</i><span>分别为</span><i>DC</i><span>，</span><i>BC</i><span>的中点，已知</span>→(AM)<span>＝</span><b><i>c</i></b><span>，</span>→(AN)<span>＝</span><b><i>d</i></b><span>，试用</span><b><i>c</i></b><span>，</span><b><i>d</i></b><span>表示</span>→(AB)<span>，</span>→(AD).</p><p class="MsoNormal"></p><p></p><p><p class="MsoNormal">②若是▱<i>ADBC</i><span>，由</span>→(CB)<span>＝</span>→(AD)<span>，得</span></p><p class="MsoNormal">(0<span>，</span>2)<span>－</span>(<span>－</span>1<span>，－</span>2)<span>＝</span>(<i>x</i><span>，</span><i>y</i>)<span>－</span>(1<span>，</span>0)<span>，</span></p><p class="MsoNormal"><span>即</span>(1<span>，</span>4)<span>＝</span>(<i>x</i><span>－</span>1<span>，</span><i>y</i>)<span>，解得</span><i>x</i><span>＝</span>2<span>，</span><i>y</i><span>＝</span>4.</p><p class="MsoNormal">∴<i>D</i><span>点的坐标为</span>(2<span>，</span>4)(<span>如图中所示的</span><i>D</i><sub>2</sub>).</p><p class="MsoNormal">③若是▱<i>ABDC</i><span>，则由</span>→(AB)<span>＝</span>→(CD)<span>，得</span></p><p class="MsoNormal">(0<span>，</span>2)<span>－</span>(1<span>，</span>0)<span>＝</span>(<i>x</i><span>，</span><i>y</i>)<span>－</span>(<span>－</span>1<span>，－</span>2)<span>，</span></p><p class="MsoNormal"><span>即</span>(<span>－</span>1<span>，</span>2)<span>＝</span>(<i>x</i><span>＋</span>1<span>，</span><i>y</i><span>＋</span>2).<span>解得</span><i>x</i><span>＝－</span>2<span>，</span><i>y</i><span>＝</span>0.</p><p class="MsoNormal">∴<i>D</i><span>点的坐标为</span>(<span>－</span>2<span>，</span>0)(<span>如图中所示的</span><i>D</i><sub>3</sub>)<span>，</span></p><p class="MsoNormal">∴以<i>A</i><span>，</span><i>B</i><span>，</span><i>C</i><span>为顶点的平行四边形的第四个顶点</span><i>D</i><span>的坐标为</span>(0<span>，－</span>4)<span>或</span>(2<span>，</span>4)<span>或</span>(<span>－</span>2<span>，</span> 0).<span></span></p></p></p><p>更多数学复习资讯，尽在数学网。</p><p><p class="p"><b>末宝带你游数学：</b></p><p class="p"><u><span>高三数学一轮复习试题：平面向量的概念</span></u></p><p class="p"><u><span>高三数学一轮复习试题：正弦定理和余弦定理</span></u></p><p class="p"><u><span>高考数学题型：椭圆与双曲线共焦点问题</span></u><span></span></p></p>
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