空间向量的正交分解及坐标表示 1 Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 2 提问:平面内的任一向量都可以用两个不共线的向量、表示(平面向量基本定理)。对于空间任意向量,有没有类似的结论呢? p ?? a ?b ?空间向量基本定理如果三个向量、、 a ?b ?c ?不共面, 那么对空间任一向量 p ??存在唯一有序实数组{x,y,z}, 使得 p xa yb zc ? ???? ??? Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 3解读: 空间任意三个不共面的向量都可以作为空间向量的一组基底用空间三个不共面的已知向量组可以线性表示出空间任意向量,且表示的结果唯一。由于零向量与任意向量都共线,与任意两个向量都共面, 所以三个向量不共面,隐含它们都不是零向量。 Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . C
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