A line has direction ratios $-18, 12, -4$ . What are its direction cosines?

-\frac{9}{11}, \frac{6}{11}, -\frac{2}{11}

Correct answerYour answer

-\frac{18}{22}, \frac{12}{22}, \frac{4}{22}

Correct answerYour answer

-9, 6, -2

Correct answerYour answer

-\frac{9}{\sqrt{11}}, \frac{6}{\sqrt{11}}, -\frac{2}{\sqrt{11}}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$\sqrt{324 + 144 + 16} = \sqrt{484} = 22$ .
$-\frac{18}{22}, \frac{12}{22}, -\frac{4}{22} = -\frac{9}{11}, \frac{6}{11}, -\frac{2}{11}$ .

Worth noting

$-9, 6, -2$ only halves the ratios; they are still ratios, not cosines.

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

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

A line has direction ratios −18,12,−4-18, 12, -4−18,12,−4. What are its direction cosines?