解题方法
1 . 如图,在斜三棱柱
中,
,且三棱锥
的体积为
.
(1)求三棱柱
的高;
(2)若平面
平面
为锐角,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131b887a0a088c760df5e17bd93bfe6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861d61d2b7b16e12fd97f870fb3fa522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/b7376265-a332-4131-9844-0dccb3b38662.png?resizew=168)
(1)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1111386161dc558c54930e35aa302737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bbdf5dbf9df96742624ada95c36146.png)
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2 . 已知圆
,过点
作圆
的两条切线,切点分别为
,且
.
(1)求
的值;
(2)过点
作两条互相垂直的直线,分别与圆
交于不同于点
的两点
,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe2a50db90fde900fc8df0838cfee04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d26e5a4e3472fd6b1dbc1ea628a3fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c0a6bf0ed3121a4b7ffb045d2ebd96.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d776a89f4fd29dccffe1040069d59ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8b8c1c96f65dd76b88502d9abec6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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3 . 如图,在四棱锥
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
为棱
的中点,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/4b635e56-de4b-4e1e-ae71-6ef75dcb94bb.png?resizew=151)
(1)求证:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9062284cdc10c304084fd63b6ca94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2845d1a90be47826b3eeb59b3a1a55f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/4b635e56-de4b-4e1e-ae71-6ef75dcb94bb.png?resizew=151)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbd7c2767c106faf27d6a97ebc8e739.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44cd09d9ad46264de4620c60370d49d.png)
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解题方法
4 . 已知正方体
的棱长为
分别是棱
和
的中点,
是棱
上的一点,
是正方形
内一动点,且点
到直线
与直线
的距离相等,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd110e5d9ab042968ec706b44e78572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
A.![]() |
B.点![]() ![]() ![]() |
C.存在点![]() ![]() ![]() ![]() |
D.动点![]() |
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5 . 已知圆
和圆
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49bce76582958794b77d4bb9fdce96fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e005da72d40c8781a41cf2c91ba580a.png)
A.圆![]() ![]() |
B.两圆公共弦所在直线的方程为![]() |
C.有且仅有一个点![]() ![]() |
D.两圆的公切线段长为![]() |
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解题方法
6 . 已知曲线
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea98e440bfde1774250b29a86a215b0d.png)
A.当![]() ![]() |
B.当![]() ![]() ![]() |
C.存在实数![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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解题方法
7 . 已知直线
与
垂直,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4ddffb98a5235f888080d1174b2a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e79e97ea8dbb64ecae5196c96b5bf14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.0 | B.0或![]() | C.![]() | D.0或![]() |
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解题方法
8 . 在空间直角坐标系
中,向量
,分别为异面直线
的方向向量,若
所成角的余弦值为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f045389aaa52422164a5782a00c68a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83fb9ac8a18e78a4c56da79514b5ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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名校
9 . 若数列
满足
,当
时,
,则称
为斐波那契数列.令
,则数列
的前100项和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644f94297a84a8edbda26f1e408444e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7885a0090b2cab1a7501209f691747c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37baa6b44a7fe407c89ca7e29af4809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644f94297a84a8edbda26f1e408444e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a52e77ca03359987cefb203a387680b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.0 | B.![]() | C.![]() | D.32 |
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10 . 已知向量
与
共线,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81958116bc8a1c3a0611cdfd592f3e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36c21aab159d8520108e8d64014b077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892560dcff6af9f66a3f735652f69dd7.png)
A.![]() | B.0 | C.2 | D.6 |
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