The equation of the line passing through origin with direction ratios $(6, 5, 7)$

\frac{x}{6} = \frac{y}{5} = \frac{z}{7}

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\frac{x}{- 1} = \frac{y}{- \sqrt{2}} = \frac{z - 7}{7}

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\frac{x - 6}{3} = \frac{y - 5}{3} = \frac{- z}{3}

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Solution

The correct option is A $\frac{x}{6} = \frac{y}{5} = \frac{z}{7}$
Equation of line passing through $(x_{1}, y_{1}, z_{1})$ and Dr`s $(a, b, c)$ is $\frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c}$
Equation of line passing through $(0, 0, 0)$ and Dr`s $(6, 5, 7)$ is $\frac{x}{6} = \frac{y}{5} = \frac{z}{7}$

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