A line makes angles of 90°, 135° and 45° with the x-, y- and z-axes. What are its direction cosines?

Question 3

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A line makes angles of $90^\circ$ , $135^\circ$ and $45^\circ$ with the $x$ -, $y$ - and $z$ -axes. What are its direction cosines?

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

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

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

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0, -\frac{1}{2}, \frac{1}{2}

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CorrectNot quiteAnswer C

Correct answer: C

Direction cosines are the cosines of the three angles.
$\cos 90^\circ = 0$ , $\cos 135^\circ = -\frac{1}{\sqrt{2}}$ , $\cos 45^\circ = \frac{1}{\sqrt{2}}$ .

Worth noting

$+\frac{1}{\sqrt{2}}$ for $135^\circ$ misses that cosine is negative in the second quadrant.

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