A line makes equal acute angles with the three coordinate axes. What are its direction cosines?

\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}

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\frac{1}{3}, \frac{1}{3}, \frac{1}{3}

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1, 1, 1

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\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}

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CorrectNot quiteAnswer A

Correct answer: A

Equal angles give $l = m = n$ , and $l^{2} + m^{2} + n^{2} = 1$ then gives $3l^{2} = 1$ .
The angles are acute, so $l = m = n = \frac{1}{\sqrt{3}}$ .

Worth noting

$\frac{1}{3}$ each makes $l + m + n = 1$ ; it is the squares that add to 1.

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

Explanation