A line makes angles α, β, with the coordinate axes. What is cos 2α + cos 2β + cos 2 ?

Three-Dimensional Geometry · Question 23 of 120

Question 23

HardOriginal question

A line makes angles $\alpha$ , $\beta$ , $\gamma$ with the coordinate axes. What is $\cos 2\alpha + \cos 2\beta + \cos 2\gamma$ ?

-1

Correct answerYour answer

0

Correct answerYour answer

1

Correct answerYour answer

3

Correct answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

$\cos 2\theta = 2\cos^{2}\theta - 1$ , so the sum is $2(\cos^{2}\alpha + \cos^{2}\beta + \cos^{2}\gamma) - 3$ .
$2 \times 1 - 3 = -1$ .

Worth noting

1 adds the three $\cos^{2}$ terms and forgets the $-1$ in each $\cos 2\theta$ .

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

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