What is the Cartesian equation of the line through $(1, -2, 3)$ parallel to the line $\frac{x - 4}{2} = \frac{y + 1}{-3} = \frac{z - 2}{6}$ ?

\frac{x - 4}{1} = \frac{y + 1}{-2} = \frac{z - 2}{3}

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\frac{x + 1}{2} = \frac{y - 2}{-3} = \frac{z + 3}{6}

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\frac{x - 1}{2} = \frac{y + 2}{-3} = \frac{z - 3}{6}

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\frac{x - 1}{4} = \frac{y + 2}{-1} = \frac{z - 3}{2}

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Worth noting

Taking $4, -1, 2$ as the direction uses the given line's point, not its direction.

Ten questions from Three-Dimensional Geometry, at your own pace.

What is the Cartesian equation of the line through (1,−2,3)(1, -2, 3)(1,−2,3) parallel to the line x−42=y+1−3=z−26\frac{x - 4}{2} = \frac{y + 1}{-3} = \frac{z - 2}{6}2x−4​=−3y+1​=6z−2​?