The equation of line equally inclined to co-ordinate axes and passing through $(- 3, 2, - 5)$ is

\frac{x + 3}{1} = \frac{y - 2}{1} = \frac{z + 5}{1}

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\frac{x + 3}{- 1} = \frac{y - 2}{1} = \frac{5 + z}{- 1}

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\frac{x + 3}{- 1} = \frac{y - 2}{1} = \frac{z + 5}{1}

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\frac{x + 3}{- 1} = \frac{y - 2}{1} = \frac{z + 5}{- 1}

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Solution

The correct option is B $\frac{x + 3}{- 1} = \frac{y - 2}{1} = \frac{5 + z}{- 1}$
Equation of line passing through $(x_{1}, y_{1}, z)$ and having $d . c . s . l, m, n$ is
$\frac{x - x_{1}}{l} = \frac{y - y_{1}}{m} = \frac{z - z_{1}}{n}$
Here $(x_{1}, y_{1}, z_{1}) \equiv (- 3, 2, - 5)$
Also line is equally inclined to co-ordinate axes.
$∴ l = - 1, m = 1, n = - 1$
$∴$ Equation of line is $\frac{x + 3}{- 1} = \frac{y - 2}{1} = \frac{z + 5}{- 1}$

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