Ta có: \(\frac{bz-cy}{a}=\frac{cx-az}{b}=\frac{ay-bx}{c}\left(1\right).\)

Nhân thêm cả tử và mẫu của (1) với a hoặc b và b;c

Từ (1) Ta lại có: \(\frac{bz-cy}{a}=\frac{abz-acy}{a^2}=\frac{bcx-baz}{b^2}=\frac{cay-cbx}{c^2}\)

                  \(=\frac{abz+acy+bcx+baz+cay+cbx}{a^2+b^2+c^2}=0\)

\(\Rightarrow\hept{\begin{cases}bx-cy=0\Rightarrow bz=cy\Rightarrow\frac{y}{b}=\frac{z}{c}\\ay-bx=0\Rightarrow ay=bx\Rightarrow\frac{y}{b}=\frac{x}{a}\end{cases}}\)

Vậy \(\frac{x}{a}=\frac{y}{b}=\frac{z}{c}\left(đpcm\right)\)

CHÚC BẠN HỌC TỐT

Rewrite the sentences so that their meanings stay the same,using the beginning given for each.

_{1.Both Mark and Stella have the same colour eyes.(different from​...)}

_{Mark's eye colour.....................}

_{2.Lan is beautiful. Hoa is beautiful, too. (as...as)}

_{I.................................}

_{3.Your voice is different from my voice. (...the same...)}

_{My voice .............................}

_{4.City life is not the same country life. ( different from...)}

_{Country life...........................}

_{5.Your house has five rooms. My house has five rooms, too. (...the same...)}

_{Your house has.....................}

_{(giúp mình làm bài này vs ạ!!!)}