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                                                                                                                类似于平面直角坐标系,定义平面斜坐标系:设数轴eqId8e15963708e9415da25069fea5906e24eqId072d7d6b911b42bc89207e72515ebf5f的交点为eqId2efda802d5534f6d92d9f8af7aaec28b,与eqId8e15963708e9415da25069fea5906e24eqId072d7d6b911b42bc89207e72515ebf5f轴正方向同向的单位向量分别是eqIdea0c0afa675249ac9f46357c36f44e8eeqIda6c2674393a5432e9234153454db9601,且eqIdea0c0afa675249ac9f46357c36f44e8eeqIda6c2674393a5432e9234153454db9601的夹角为eqIdf9db0aee08264a238b9741675591065e,其中eqId5a06bd3b6e0b4df5b82d877faf48b31a,由平面向量基本定理:对于平面内的向量eqIdebd2c49c11694af6b3faec0bcc4f0b27,存在唯一有序实数对eqId250f7fb784d24e0cafe915042cd755cf,使得eqId6ed553c331884100a0b1aef753f7506f,把eqId250f7fb784d24e0cafe915042cd755cf叫做点eqIdd7be5abad1e34f6db17a56660de8d54f在斜坐标系eqId2272a344734c4fb088737b84294f7219中的坐标,也叫做向量eqIdebd2c49c11694af6b3faec0bcc4f0b27在斜坐标系eqId2272a344734c4fb088737b84294f7219中的坐标,记为eqId0aa654b03e9b49a5bae2ba96eb4b8007,在平面斜坐标系内,直线的方向向量、法向量、点方向式方程、一般式方程等概念与平面直角坐标系内相应概念以相同方式定义,如eqIdc0d4362b410346839841fc204dacd181时,方程eqId7499ca8fb6c64fe4938bb280d620fcc2表示斜坐标系内一条过点eqId1281c2deb36f4f68ad0b3b134928c713,且方向向量为eqIdcd5b60f0f4654cc69337b68261bf8233的直线.
                                                                                                                figure
                                                                                                                (1)若eqIdc0d4362b410346839841fc204dacd181eqId11469979b568428d9b2785baff554f93eqId177504291cfd40e08d1b783995f84ad2,求eqIdfc1ad564f06546869e44d6a84b22b73a
                                                                                                                (2)若eqIdc0d4362b410346839841fc204dacd181,已知点eqId25b63077c8ca4563ba82dfd04ed69343和直线eqIde443ffd0acbf45fc91f59b20e372a39f
                                                                                                                ①求eqId417e80f1349244878d01fe90e0891f5f的一个法向量;
                                                                                                                ②求点eqIdcc614bd3390c4d028df189b234dcc351到直线eqId417e80f1349244878d01fe90e0891f5f的距离.
                                                                                                                更新:2019/12/2难度系数:0.65题型:解答题组卷:11次
                                                                                                                已知两个不相等的非零向量eqIdbfdcb35337334952b6d7ceab2f7c8afd,两组向量eqIde5d35bdc5cb74b80a1a1acdafcb78f39eqIdb64f7679e39f4e0d817902382872a77d均由2个eqIdf087b35a5011425daaafbf14a5e61064和3个eqId5f16eb46594d47b58ffc973b5cc2dd0d排列而成。记eqId4cde2abd84d84e99bcfbc9c4a4c61829,则eqIdbaec8f9edcf54a70a8797f93357849da表示eqId1b7d8b87b50e4cfdbf89d48980209a52所有可能取值中的最小值,有以下结论:①eqId1b7d8b87b50e4cfdbf89d48980209a52有5个不同的值;②若eqId3354fe4e9ad04d1ea1780fcce00b9577,则eqIdbaec8f9edcf54a70a8797f93357849daeqId4d9174dfff5b47369901aef8b738e75c无关;③若eqId28860dd5f35e4263bec9d9f2c11f2375,则eqIdbaec8f9edcf54a70a8797f93357849daeqIdf180c3fedfe44bb4902ca671d7c080d0无关;④若eqId870ef448072f4464a8fc8644f78b6e21,则eqId358f94a9c3d54a18aa184a19b5e8d835;⑤若eqId75faa753c9fd4a55815858145dbeae63,则eqIdf087b35a5011425daaafbf14a5e61064eqId5f16eb46594d47b58ffc973b5cc2dd0d的夹角为eqIdb47bf79338b1478a89eac53d16970cdf,则正确的结论的序号的是(??)
                                                                                                                A.①②④B.②④C.②③D.①⑤
                                                                                                                更新:2019/11/21难度系数:0.4题型:单选题组卷:30次
                                                                                                                定义两个非零平面向量的一种新运算eqId99c0cfe3e19340d399fb466dc04b276a,其中eqIda95b97d4604449da978d2f6e0c0524d7表示eqIda59ccdbd07dd4c9cbf71bce78c339a93的夹角,则对于两个非零平面向量eqIda59ccdbd07dd4c9cbf71bce78c339a93,下列结论一定成立的有(??)
                                                                                                                A.eqIdaa64ebd16a27427e980193ba83ac149feqIdafbffe7e96ba4e8ba0c33fc164414230方向上的投影为eqIdb3ca344ac6d743e4ba755366d2fc348b
                                                                                                                B.eqId1461a5181fcf4656b50beec7a391be49
                                                                                                                C.eqId67c0c945960e43698586ab6da65f8f8f
                                                                                                                D.若eqIdcde2bc30a3104911b4c3b2bd656567e0,则eqIdaa64ebd16a27427e980193ba83ac149feqIdafbffe7e96ba4e8ba0c33fc164414230平行
                                                                                                                更新:2019/6/11难度系数:0.65题型:多选题组卷:383次
                                                                                                                已知在平面直角坐标系中,点ABC的坐标分别为A(cosα,sinα),B(2,0),C(0,2),α∈(0,π).
                                                                                                                (1)若eqId0499606d48924becad107915f517695b,求α的值;
                                                                                                                (2)若eqId4734960cea644ff59d97e858ed4d0bfc,求eqIda86505723afd4ae5ba2070dd95e59f0b的值.
                                                                                                                更新:2019/3/19难度系数:0.4题型:解答题组卷:459次
                                                                                                                eqId2afa2d9bb3884033b198af61485b188a是两个不共线的非零向量.
                                                                                                                (1)设eqId09ffbe09ceda4fc8ba1e08bea2f8618feqId285142f3b9934e55ab2bf99b76ae781eeqId4845348009b84d43b33e37369def3047,那么当实数t为何值时,A,B,C三点共线;
                                                                                                                (2)若eqIdb354a99a9a2a4e52b32ea4b700801f7aeqIda4de65a0694942e3907b7be46cb8abdfeqIdbf80e33f8af0497793eeb1eb2a0e416eeqId26d0383ebc3f44c2984e80b88390a5f5的夹角为60°,那么实数x为何值时eqId2e3ed7d01a944924a84575c30742e8bf的值最小?最小值为多少?
                                                                                                                更新:2019/3/19难度系数:0.65题型:解答题组卷:423次
                                                                                                                已知eqIdbfdcb35337334952b6d7ceab2f7c8afd是非零向量,它们之间有如下一种运算:eqId8a4845a3e52e4cbf8a20a715d5483890,其中eqId317624d74b034b28a00d22a985fc86c5表示eqIdbfdcb35337334952b6d7ceab2f7c8afd的夹角.下列命题中真命题的个数是
                                                                                                                eqIdb2f5509143e44291ae9c204af45fac4f;②eqIdaf14f5a34541439ba60a6e909c68bfd9;③eqId36ccb0c364044416963ce87b170faf64
                                                                                                                eqId2c48e6b546814f4e8c59c7b50bdc9d07;⑤若eqId611d777de21c4794b6175107b25371df,则eqIde18ebf7e63c94fa6be535bb98322c5aa
                                                                                                                A.2B.3
                                                                                                                C.4D.5
                                                                                                                更新:2018/9/27难度系数:0.4题型:单选题组卷:313次
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