Direction ratios of two lines $a, b, c$ and $1 / b c, 1 / c a, 1 / a b$ . Then the lines are _______

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Solution

If direction ratios of two lines $a, b, c$ and $\frac{1}{b c}, \frac{1}{c a}, \frac{1}{c b}$
then, lines are
$\begin{matrix} a x + b y + c z = 0 \to (i) \Rightarrow \frac{x}{b c} + \frac{y}{c a} + \frac{z}{c b} = 0, \end{matrix}$

Multiply by $a b c$ on both side
$\begin{matrix} \Rightarrow \frac{a b c x}{b c} + \frac{a b c y}{c a} + \frac{a b c z}{b c} = 0 a x + b y + c z = 0. \end{matrix}$

Hence, this is the answer.

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