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www.js1392.com:安徽省六安市舒城中学2017-2018学年高二数学(理)暑假作业 第二十天 Word版含答案

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2017-2018 学年第 20 天 平面向量 【课标导航】平面向量的概念、运算及应用 一、选择题最新试卷十年寒窗苦,踏上高考路,心态放平和,信心要十足,面对考试卷,下笔如有神,短信送祝福,愿你能高中,马到功自成,金榜定题名。 1.已知点 A ?1,3? , B ? 4, ?1? , 则与向量 AB同方向的单位向量为 A. ? ,- ( ) ?3 ?5 4? ? 5? B. ? ,- ? ?4 ?5 3? 5? C. ? ? , ? ? 3 4? ? 5 5? D. ? ? , ? 2. 已知点 O 是平面 ABC 上一定点,若动点 P 满足 OP = OA + l ( AB + AC) ,那么动点 P 的轨迹一定过△ABC 的 ( ) A.重心 ? 4 3? ? 5 5? B.垂心 C.外心 D.内心 3. 已知点 O 是平面 ABC 上一定点,若动点 P 满足 OP ? OA ? ? ( AB | AB | | AC | ? AC ) ,那么动点 P 的轨迹一定过△ABC 的 ( ) A.重心 B.垂心 C.外心 D.内心 4 . 在边长为 1 的正六边形 ABCDEF 中 , 记以 A 为起点 , 其余顶点为终点的向量分别为 a1 , a2 , a3 , a4 , a5 ;以 D 为起点,其余顶点为终点的向量分别为 d1, d2 , d3 , d4 , d5 .若 m, M 分别为 ( ai ? a j ? ak ) ? ( d r ? d s ? d t ) 的最小值、最大值, 其中 {i, j, k} ? {1, 2,3, 4,5} , {r , s, t} ? {1, 2,3, 4,5} ,则 m, M 满足 A. m ? 0, M ? 0 D. m ? 0, M ? 0 5 . 设 ?ABC, P 0 是边 AB 上一定点 , 满足 ( ) B. m ? 0, M ? 0 C. m ? 0, M ? 0 P0 B ? 1 AB , 且对于边 AB 上任一点 P , 恒有 4 ( ) PB ? PC ? P 0B ? P 0C .则 A. ?ABC ? 90 0 B. AC ? BC 0 C. AB ? AC D. ?BAC ? 90 6.在四边形 ABCD 中, AC ? (1, 2) , BD ? ( ?4, 2) ,则四边形的面积为 ( ) A. 5 7.在平面上, AB1 B. 2 5 C.5 D.10 1 ? AB2 , OB1 ? OB2 ? 1 , AP ? AB1 ? AB2 .若 OP ? ,则 OA 的取值 2 ? 5 7? ? 2 , 2 ? ? ? 范围是( ) A. ? 0, ? ? ? 5? ? 2 ? B. ? C. ? ? 5 ? , 2 ? ? 2 ? ? D. ? ? 7 ? , 2 ? ? 2 ? ? ( ) 8 .已知 a, b 是单位向量, a b ? 0 .若向量 c 满足 c ? a ? b ? 1, 则 c 的取值范围是 , 2+2 ? A. ? 2-1, ? ? , 2+1? C. ?1, ? ? 二、填空题 , 2+1? B. ? 2-1, ? ? , 2+2 ? D. ?1, ? ? 9.已知正方形 ABCD 的边长为 2 , E 为 CD 的中点,则 AE BD ? _______. 10 .已知向量 AB 与 AC 的夹角为 120 °,且 AB ? 3 , AC ? 2 , 若 AP ? ? AB ? AC , 且 AP ? BC ,则实数 ? 的值为__________. 11.设 e1 , e2 为单位向量,非零向量 b ? xe1 ? ye2 , x, y ? R ,若 e1 , e2 的夹角 为 大值等于________. 12 设 O 点在 ?ABC 内部,且有 OA ? 2OB ? 3OC ? 0 ,则 ?ABC 的面积与 ?AOC 的面积 的比为 三、解答题 13.在平面直角坐标系 xOy 中,点 A(-1,-2)、B(2,3)、C(-2,-1). (1)求以线段 AB、AC 为邻边的平行四边形两条对角线的长; (2)设实数 t 满足( AB ? t OC )· OC =0,求 t 的值. |x| ? ,则 的最 6 |b| uur uu u r uuu r r 3 3 x x ? x,sin x), b ? (cos , ? sin ), 且x ? [0, ], 求 2 2 2 2 2 3 (1) a ? b及 | a ? b | ;(2)若 f ( x) ? a ? b ? 2? | a ? b | 的最小值是 ? , 求?的值; 2 14.已知向量 a ? (cos 15.设向量 a ? (1, cos2? ),b ? (2,1), c ? ( 4 sin ? ,1), d ? ( sin ? ,1) ,其中 ? ? (0, (1)求 a ? b ? c ? d 的取值范围; (2)若函数 f ( x) ?| x ? 1 |,比较f (a ? b)与f (c ? d ) 的大小 1 2 ? 4 ). 第二十天 1-8AADDBCDB 9.2 10. 7 12 11.2 12.3 13. (1)BC= 4 2 、AD= 2 10 (2) t ? ? 2 11 5 2 14(1) a ? b ? cos 2 x , a ? b ? a ? 2a ? b ? b ? 2 ? 2cos 2 x ? 2cos x , x ? [0, ] π 2 (2) λ? 1 2 15.(1) a ? b ? c ? d的取值范围是(0, 2) (2) f (a ? b) ? f (c ? d )

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