$$\Rightarrow \overrightarrow{HC}=\overrightarrow{HA'}+\overrightarrow{HB'}$$
Ta có :
$$\frac{CB'}{AH}=\frac{B_1C}{AB_1}=\frac{a\ cosC}{c\ cosA}\Rightarrow
\overrightarrow{HA'}=-\overrightarrow{CB'}=-\frac{a\ cosC}{c\ cosA}\overrightarrow{HA} (1)$$
Tương tự
$$\overrightarrow{HB'}=-\overrightarrow{CA'}=-\frac{b\ cosC}{c\ cosB}\overrightarrow{HB} (2)$$
Từ (1) và (2) suy ra
$$\overrightarrow{HC}=-\frac{a\ cosC}{c\ cosA}\overrightarrow{HA}-\frac{b\ cosC}{c\ cosB}\overrightarrow{HB}$$
$$\Leftrightarrow \frac{a}{\ cosC}\overrightarrow{HA}+\frac{b}{\ cosB}\overrightarrow{HB}+\frac{c}{\ cosC}\overrightarrow{HB}=\overrightarrow{0}$$
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