The equation of straight line passing through $(a, b, c)$ and $(a - b, b - c, c - a)$ , is

\frac{x - a}{a - b} = \frac{y - b}{b - c} = \frac{z - c}{c - a}

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\frac{x - a}{b} = \frac{y - b}{c} = \frac{z - c}{a}

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\frac{x - a}{a} = \frac{y - b}{b} = \frac{z - c}{c}

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\frac{x - a}{2 a - b} = \frac{y - b}{0} = \frac{z - c}{2 c - a}

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Solution

The correct option is B $\frac{x - a}{b} = \frac{y - b}{c} = \frac{z - c}{a}$
Co-ordinates of points are: $(a, b, c)$ and $(a - b, b - c, c - a)$
$∴$ DR = $(a - b - a, c - c - b, c - a - c)$
$= (- b, - c, - a)$
Equation of line through $(a, b, c)$ with DR = $(- b, - c, - a)$
$\Rightarrow \frac{x - a}{- b} = \frac{y - b}{- c} = \frac{z - c}{- a}$
$\Rightarrow \frac{x - a}{b} = \frac{y - b}{c} = \frac{z - c}{a}$
option B is correct answer

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\frac{y}{b + c - a} = \frac{z}{c + a - b} = \frac{x}{a + b - c}

x + y + z \neq 0

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