Tích vô hướng

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vitconvuitinh

Xét tam giác ABM, cát tuyến NC:
Theo định lí Mê-nê-la-uýt
[TEX]\frac{IA}{IM}.\frac{CM}{CB}.\frac{NB}{NA}=1[/TEX]
\Rightarrow [TEX]\frac{IA}{IM}=\frac{3}{4}[/TEX]
[TEX]\vec{BI}.\vec{CN}=(\frac{3}{7}\vec{BM}+\frac{4}{7}\vec{BA})(\vec{BN}-\vec{BC})=\frac{3}{7}BM.BN.cos60-\frac{3}{7}BM.BC.cos0+\frac{4}{7}BA.BN.cos0-\frac{4}{7}BA.BC.cos60[/TEX]
\Rightarrow [TEX]\frac{3}{7}.\frac{1}{3}a(\frac{1}{3}a-a)+\frac{4}{7}a(\frac{2}{3}a-\frac{1}{2}a)=0[/TEX]
\Rightarrowđpcm
 
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