Ta có :
` (bz-cy)/a= (a(bz-cy))/a^2 = (abz - acy)/a^2`
`(cx -az)/b = (b(cx -az))/b^2 = (bcx - abz)/b^2`
`(ay-bx)/c = (c(ay- bx))/c^2 = (acy - bcx)/c^2`
`=> (abz - acy)/a^2 = (bcx - abz)/b^2= (acy - bcx)/c^2`
Theo tính chất dãy tỉ số bằng nhau :
`=> (abz - acy)/a^2 = (bcx - abz)/b^2= (acy - bcx)/c^2 = (abz - abz + bcx - bcx + acy - acy)/(a^2 + b^2 + c^2) = 0`
`=>` $\begin{cases} a(bz -cy) =0 \\ b(cx -az) =0 \\ c(ay-bx) = 0 \end{cases}$
`=>` $\begin{cases} bz = cy \\ cx = az \\ ay = bx \end{cases}$
`=>` $\begin{cases} \dfrac{b}{y} = \dfrac{c}{z} \\ \dfrac{a}{x} = \dfrac{c}{z} \\ \dfrac{b}{y} = \hat{a}{x} \end{cases}$
`=> a/x = b/y =c/z` ( ĐPCM)
