Question

cho a,b,c,x,y,z thỏa mãn:

\(\frac{x}{a}=\frac{y}{b}=\frac{z}{c}\)

chừng minh:   \(\frac{bz-cy}{a}=\frac{cx-az}{b}=\frac{ay-bx}{c}\)

Answer 1

\(\frac{x}{a}=\frac{y}{b}\Rightarrow bx=ay\Rightarrow ay-bx=0\Rightarrow\frac{ay-bx}{c}=0\left(1\right)\)

\(\frac{x}{a}=\frac{z}{c}\Rightarrow cx=az\Rightarrow cx-az=0\Rightarrow\frac{cx-az}{b}=0\left(2\right)\)

\(\frac{y}{b}=\frac{z}{c}\Rightarrow cy=bz\Rightarrow bz-cy=0\Rightarrow\frac{bz-cy}{a}=0\left(3\right)\)

\(\text{Từ (1);(2) và (3) suy ra: }\frac{bz-cy}{a}=\frac{cx-az}{b}=\frac{ay-bx}{c}=0\)