Question

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Answer 1

\(\dfrac{ay-bx}{c}=\dfrac{cx-az}{b}=\dfrac{bz-cy}{a}\\ \Rightarrow\dfrac{acy-bcx}{c^2}=\dfrac{bcx-abz}{b^2}=\dfrac{abz-acy}{a^2}=\dfrac{acy-bcx+bxc-abz+abz-acy}{a^2+b^2+c^2}=0\\ \Rightarrow\left\{{}\begin{matrix}ay-bx=0\\cx-az=0\\bz-cy=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}ay=bx\\cx=az\\bz=cy\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{a}=\dfrac{y}{b}\\\dfrac{x}{a}=\dfrac{z}{c}\\\dfrac{y}{b}=\dfrac{z}{c}\end{matrix}\right.\\ \Rightarrow\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}\)