What are the direction cosines of the rod,…

What are the direction cosines of the rod, taken from O to P?

Question 8

EasyOriginal question

A hall's corner is the origin $O$ , with the floor edges along the $x$ - and $y$ -axes and the vertical edge along the $z$ -axis; lengths are in metres. A straight rod runs from $O$ to the point $P(6, 2, 9)$ .

What are the direction cosines of the rod, taken from $O$ to $P$ ?

\frac{6}{17}, \frac{2}{17}, \frac{9}{17}

Correct answerYour answer

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

Correct answerYour answer

6, 2, 9

Correct answerYour answer

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

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

The rod is $\sqrt{36 + 4 + 81} = \sqrt{121} = 11$ long.
Its direction cosines are $\frac{6}{11}, \frac{2}{11}, \frac{9}{11}$ .

Worth noting

$\frac{6}{17}, \frac{2}{17}, \frac{9}{17}$ divides by $6 + 2 + 9 = 17$ , not by the length 11.

Concept: Direction cosines of the line through two points
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsDirection cosines of a line

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

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

What are the direction cosines of the rod, taken from O to P?

Question 8

Explanation