A line $L$ has direction ratios $6, -2, -3$ . Which of the following statements are true?
I. The direction cosines of $L$ are $\frac{6}{7}, -\frac{2}{7}, -\frac{3}{7}$ , or these three with their signs reversed.
II. $L$ is perpendicular to the line with direction ratios $1, 3, 0$ .
III. $L$ is parallel to the line with direction ratios $12, 4, 6$ .
IV. The direction cosines of $L$ add up to 1.

I and II onlyCorrect answerYour answerI, II and III onlyCorrect answerYour answerI and III onlyCorrect answerYour answerII and IV onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$\sqrt{36 + 4 + 9} = 7$ , so I is true; $6(1) + (-2)(3) + (-3)(0) = 0$ , so II is true.
$12, 4, 6$ is not a multiple of $6, -2, -3$ , so III is false; $\frac{6 - 2 - 3}{7} = \frac{1}{7}$ , so IV is false.

Worth noting

III fails on the signs: twice $6, -2, -3$ is $12, -4, -6$ .

Concept: Direction ratios and direction cosines
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsDirection cosines of a line

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