设向量 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 不共面,则空间任一向量 [tex=0.571x1.0]QDHYLzpRIwhOrWBqGonCgg==[/tex] 可以分解为向量 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 的线性组合式 :[tex=12.0x2.714]EKa3tlBXxUzrZm3G0NxoF4BEV+uQk9RXqZ1Xf9B11fEMxcw7CPLWJYzej2ceFrWCEkxTOfFyaUAzMJbZOHFXTyonbonaBRPx9H1FWIo65q+dtzg9XHmNztxgcnkbq3yq[/tex].

2022-11-04

设向量 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 不共面,则空间任一向量 [tex=0.571x1.0]QDHYLzpRIwhOrWBqGonCgg==[/tex] 可以分解为向量 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 的线性组合式 :[tex=12.0x2.714]EKa3tlBXxUzrZm3G0NxoF4BEV+uQk9RXqZ1Xf9B11fEMxcw7CPLWJYzej2ceFrWCEkxTOfFyaUAzMJbZOHFXTyonbonaBRPx9H1FWIo65q+dtzg9XHmNztxgcnkbq3yq[/tex].

答案：

证明 1：因 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 不共面，则对于空间任一向量 [tex=0.571x1.0]QDHYLzpRIwhOrWBqGonCgg==[/tex] 有[tex=5.786x1.214]YZQdkLgT0t9pJYKp6h+fa0TowLLJr8mOMul3nYMhVtk=[/tex]因在上向量等式中待定常数有三个，为先求出一个，必消掉两个,为此在上式两端分别与向量 [tex=2.143x1.143]jp8DvzKn3+56E3kfD79X2w==[/tex] 作数量积, 即在等式两端作混合积,消掉 [tex=2.0x1.286]akiPOM+OMRREkwegej0VpQ==[/tex] , 求得 [tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex] :[tex=24.5x1.357]De166nmeTkb4C/83+ZZH23sSAxFe+eRRp11PLOogQEiS1FXqVfexKt9hau3GTbTzjvSQCWs14/ORQoLJlLC0LpyiyWEi+eLsxQpeDAgJUKMa+AL3PKVSM3aCPQnuocOlFUzsJRxydN1R2jLdxBX2nBe5S4AJf48FMF/CfKia4zo3Y/WLj0UJpW+wliGPo36auu7iLgWaZIB6m4Un3y5CZ9TMWRzSDbpwz/eQNYjeo/t3C3DSxs7opQG4E0IiQYzB78wEhQCdfLiNRLR8K5Fz5exUOk2/yybxwB4rHdeQclAQXSHZ48AvL7xmkQofl81X[/tex].因 [tex=12.286x1.357]NeoTBlf1CmkUoMf07Si5dP68/LuhlDlAPtP6SWebBQkOtdnM0/ZZ2ml3aQ4I69Hes6rZdgGW4jHeZyfRCr28XOIQLn5c+bZ+/nFuwJed2mL/I7QJZbSjl12tFD8amZHHKI/Q4YRoeqe/ic2Xt42yJw==[/tex],故 [tex=5.571x1.357]8m+hvUjVldCAOKRWlLCUPV+xAinoUnTj6b3TS+dd/Ko=[/tex] 又因 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 不共面,故 [tex=3.929x1.286]N9O05afPLLpjfBI7LxWdb6BXHsDQReXkO4eMWN4I5c4=[/tex] 所以[tex=12.286x1.357]eETTREvNZp242K+N8tJVCt2oarKTEtMnmm1lPNMMn77Q4oskbPmYdLOK6WaJBH1Up0iqNPfJwWuD1fuJ1dsytPGp++vbGsK9zZi/8pGTA4845mWGEEBzeuWVtYzJ3X3uLOxR3IkHVFcPhxLqj8LQQmCHGvgWJV+wZWPpwKp6WI8=[/tex],同理可得 [tex=22.214x1.357]JyWUoZA/XsJGita8fpi0awqiBbhF46UytQCDMuSmdZZFBgWyI+7Iim1NTvj2ADSqAD+m97RM6Cj+XVz8bIgw+L4CpH/nJztUbJhaZr8E0ZxDcZpRErGfE0jlAfNzeJQq+Mm/yCvoRB6MnqUAG9y7ov7P9N17rCR5k66gB2S6/3l7o7Swme28Y6us3f3IZxXcWVBBWavuKGJph6lsAhpzP4ng3+0NIGUC/TOsx0HaWgw=[/tex]证明 2：因为 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 不共面，则 [tex=6.071x1.214]mtNakJ5iqpglNluiF9FPqIdAnVDQNGSYQu8r7JZMllY=[/tex]在空间直角坐标系下,设 [tex=24.143x1.357]I7XvfhDm7qmNlahUCNH41SuUoJ+a9KNgNcuJNqsnOiVHRiAUQEtjQwxRCuq1g1uujgA7ulL6Ha7ipQiwRyTF+u20jQmIkiJGsPZz0jCaAD/YP/rjSUXqhyzX1gPe4SsIMQmyVlnCdWwdhNDRvpkKgAUl058SqtC+aBt1U3DqCHHEysDsZ2con9z9IgqR/000BJmb08D9EYmf39wzCDEWGA==[/tex], 代入上式得方程组[tex=9.071x4.214]GE56u9QCDTqcLxZ66HADypfwST5dGTIruQT/Y3Bc0eQOG6QpCO4h6hzqrdzNOQrYip7KU4R5jcoShRNZhX+4zbW0micfEypGVqIDLUxcHPgcqpQvKMqkxby63P7jXLAhuD16+uPefug6eEiOfUuTDxuLMpf7Dba0FlcQHwqbZyMtS5y3zr2vhIzT6FWW4h/hEQ3m852iVDK54bAWb37YSQ==[/tex]由克莱姆法则得上方程组的解为[tex=29.357x7.214]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[/tex][tex=26.571x1.357]qFg5zSSfTAZkWd7dT8TGaEWJ1jjmezGh/DNANqXlmsr2vfQCsvY1uHAfUN/rnz26fwsULTv8MRKrjL6wuQ5FGEc9/EKTeeNePijuWG58G9DHR4Us/zjjbVRmH+mz+l4JsHRL1vMbt+hxFP/dQHtHARnZF22yuRjqD1clMohon5kZ6TPLBQ5IV1OhCy7yCbk4lEdeOb6fMyb/P5vSAav1fyYun9uoypaaq0Wl2gBNGxxFopXeBlCEEcfg3nSjFIoTMmNp9P7+Cx7H5kcsEjOjxIHDIcqcj8eetxTWTvLD2jrrffcieQC4jVs052vjngBK[/tex]

举一反三

内容

0
试用向量法证明: 设[tex=2.286x1.214]XFQeabN7z0jBrIlKJ5wKtg==[/tex] 三个向量不共面，若向量[tex=0.5x0.786]U5O66aolbR1y5vuKrQbXNA==[/tex] 满足[tex=8.643x1.214]pc0d189WKHGaQSOPYulcLmE4eqh46zHXogpUh9o/G48hoPRgmvT3zQuY3+BJXWwx[/tex] 则[tex=2.071x1.0]S58FaUSfom9xiguEYLzV4A==[/tex] 试证之.
1
设向量 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex]. 若[tex=4.786x1.143]vIoIF5/XALHvQTUrZgGrog==[/tex], 且[tex=7.5x1.357]D3zuJPjeH86ZxkvRhehs1Fd85S1i9OdSmR1xhgzR7AY=[/tex], 则[tex=6.0x1.143]eBhIDbl3KZGg83K6KN90vrELTlmxZpAFu0N4jKD3X2SJKE/S8DN6GH93u/EWE/U3[/tex][input=type:blank,size:6][/input]
2
以4，9，1为为插值节点，求\(\sqrt x \)的lagrange的插值多项式 A: \( {2 \over {15}}(x - 9)(x - 1) + {3 \over {40}}(x - 4)(x - 1) + {1 \over {24}}(x - 4)(x - 9)\) B: \( - {2 \over {15}}(x - 9)(x - 1) + {3 \over {40}}(x - 4)(x - 1) + {1 \over {24}}(x - 4)(x - 9)\) C: \( - {2 \over {15}}(x - 9)(x - 1) + {3 \over {40}}(x - 4)(x +1) + {1 \over {24}}(x - 4)(x - 9)\) D: \( - {2 \over {15}}(x - 9)(x - 1) + {3 \over {40}}(x - 4)(x - 1) - {1 \over {24}}(x - 4)(x - 9)\)
3
9判别下列函数是否是周期函数,若是周期函数,求其周期 :(1) [tex=8.357x1.357]jijpvC8Aw74QOOOJh5Va05j3PtA64Pms1Q5qDGlqeN4=[/tex](2) [tex=5.643x1.357]TG5DUF3HrCbhIJWDEcp5Pj9u3e2PUgpbN4NJQ6DZXLw=[/tex](3) [tex=5.714x1.357]SBxtvKszj8+jJcycMEKn5vqfhi5GLWqH4Gac9QRbIHc=[/tex](4) [tex=6.929x1.357]NZ5EVFRfE4pFsgkbEOhFkNg5/qZx8geAT5eL+yzbq1Q=[/tex]
4
设 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 是三个不共面的向量,则 [tex=3.714x1.357]XBtZiWlLYlOq3xHpqgCN/D/U4kbyliDB6csmB5YS3xs=[/tex] 等于未知类型：{'options': ['[tex=3.714x1.357]W2LjlhU5cw84mjAEfP5ZswT9NTJ0nolT8nZpZuhddMU=[/tex]', '[tex=3.714x1.357]CVznmF00DXylv4EWhqLWTtmIq45uIjGGLXV7+xVxh2Q=[/tex]', '[tex=3.714x1.357]rA3xrIbC9+pxL/1GFB84hFVFmlwqGlo8fpYUzaesTY0=[/tex]', '[tex=3.714x1.357]PbSk6EZxrKe5ijCc0aOITJEYMOVWNBLaovaJEEUlxxg=[/tex]'], 'type': 102}