`text{Ta có :}`
$\dfrac{bz - cy}{a}$ `=` $\dfrac{cx - az}{b}$ `=` $\dfrac{ay - bx}{c}$
`=>` $\dfrac{ x . ( bz - cy )}{x . a}$ `=` $\dfrac{ y . ( cx - az )}{y . b}$ `=` $\dfrac{ z . ( ay - bx)}{z . c}$
`=>` $\dfrac{xbz - xcy}{x . a}$ `=` $\dfrac{ycx - yaz}{y . b}$ `=` $\dfrac{zay - zbx}{z . c}$
`text{Áp dụng tính chất dãy tỉ số bằng nhau , ta có :}`
$\dfrac{xbz - xcy}{x . a}$ `=` $\dfrac{ycx - yaz}{y . b}$ `=` $\dfrac{zay - zbx}{z . c}$
`=` $\dfrac{xbz - xcy + ycx - yaz + zay - zbx }{xa + yb + zc}$
`=` $\dfrac{0}{xa + yb + zc}$
`=` `0`
* `text{Ta có :}`
$\dfrac{xbz - xcy}{x . a}$ `=` `0`
`=> xbz - xcy = 0`
`=> xbz = xcy`
`=> bz = cy`
`=> y/b = z/c` `(1)`
* `text{Ta có :}`
$\dfrac{ycx - yaz}{y . b}$ `=` `0`
`=> ycx - yaz = 0`
`=> ycx = yaz`
`=> cx = az`
`=> x/a = z/c` `(2)`
Từ `(1)` và `(2)`
`=> x/a = y/b = z/c`
`=> a/x = b/y = c/z`
