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The equation of the plane through the origin containing the line $\frac{x - 1}{5} = \frac{y - 2}{4} = \frac{z - 3}{5}$ is.

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$2 x + 5 y - 6 z = 0$

$x + 5 y - 5 z = 0$

$x - 5 y + 3 z = 0$

$x + y - z = 0$

answer is C.

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Detailed Solution

A general point $(5 r + 1, 4 r + 2, 5 r + 3)$ on the line should satisfy the required plane, which is satisfied by $x - 5 y + 3 z = 0$ .

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