已知三个非零向量m,n,p不共面,a=m+2n+3p,b=3m+2n+p,c=7m+8n+9p,求证:a,b,c三个向量共面.
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![已知三个非零向量m,n,p不共面,a=m+2n+3p,b=3m+2n+p,c=7m+8n+9p,求证:a,b,c三个向量共面.](/uploads/image/z/8857419-51-9.jpg?t=%E5%B7%B2%E7%9F%A5%E4%B8%89%E4%B8%AA%E9%9D%9E%E9%9B%B6%E5%90%91%E9%87%8Fm%2Cn%2Cp%E4%B8%8D%E5%85%B1%E9%9D%A2%2Ca%3Dm%2B2n%2B3p%2Cb%3D3m%2B2n%2Bp%2Cc%3D7m%2B8n%2B9p%2C%E6%B1%82%E8%AF%81%EF%BC%9Aa%2Cb%2Cc%E4%B8%89%E4%B8%AA%E5%90%91%E9%87%8F%E5%85%B1%E9%9D%A2.)
已知三个非零向量m,n,p不共面,a=m+2n+3p,b=3m+2n+p,c=7m+8n+9p,求证:a,b,c三个向量共面.
已知三个非零向量m,n,p不共面,a=m+2n+3p,b=3m+2n+p,c=7m+8n+9p,求证:a,b,c三个向量共面.
已知三个非零向量m,n,p不共面,a=m+2n+3p,b=3m+2n+p,c=7m+8n+9p,求证:a,b,c三个向量共面.
逆向思维:如果a,b,c三个向量共面,必定存在一组数r、s、t使得ra+sb+tc=0
所以有r+3s+7t=0,2r+2s+8t=0,3r+s+9t=0,联立方程组可解得rst的值,所以当rst取这个值的时候abc三个向量共面