Question

Cho \(\dfrac{bz-cy}{a}\)=\(\dfrac{cx-az}{b}\)=\(\dfrac{ay-bx}{c}\). Chứng minh \(\dfrac{x}{a}\)=\(\dfrac{y}{b}\)=\(\dfrac{z}{c}\)

Answer 1

Lời giải:

Áp dụng TCDTSBN:

$\frac{bz-cy}{a}=\frac{cx-az}{b}=\frac{ay-bx}{c}$

$=\frac{bza-cya}{a^2}=\frac{cxb-azb}{b^2}=\frac{ayc-bxc}{c^2}$

$=$\frac{bza-cya+cxb-azb+ayc-bxc}{a^2+b^2+c^2}=\frac{0}{a^2+b^2+c^2}=0$

$\Rightarrow bz-cy=cx-az=ay-bx=0$

$\Rightarrow bz=cy; cx=az$

$\Rightarrow \frac{b}{y}=\frac{c}{z}; \frac{x}{a}=\frac{c}{z}$

$\Rightarrow \frac{x}{a}=\frac{b}{y}=\frac{c}{z}$