Which is the Cartesian equation of the line through $(4, -2, 1)$ that makes equal acute angles with the coordinate axes?

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

Correct answerYour answer

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

Correct answerYour answer

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

Correct answerYour answer

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

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Equal acute angles give direction cosines $\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$ , so the direction ratios are $1, 1, 1$ .
Through $(4, -2, 1)$ : $\frac{x - 4}{1} = \frac{y + 2}{1} = \frac{z - 1}{1}$ .

Worth noting

$\frac{x - 4}{4} = \frac{y + 2}{-2} = \frac{z - 1}{1}$ uses the point's coordinates as the direction.

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

Which is the Cartesian equation of the line through (4,−2,1)(4, -2, 1)(4,−2,1) that makes equal acute angles with the coordinate axes?