A bead on the rod is 4.5 m above the floor.

Question 17

MediumOriginal 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 $P(6, 2, 9)$ .

A bead on the rod is 4.5 m above the floor. How far is it from $O$ , measured along the rod?

\frac{81}{22}

mCorrect answerYour answer4.5 mCorrect answerYour answer5.5 mCorrect answerYour answer8.25 mCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

A point of the rod at distance $s$ from $O$ is at height $s \times \frac{9}{11}$ .
$s \times \frac{9}{11} = 4.5$ gives $s = 5.5$ m.

Worth noting

4.5 m is the height; the rod slants, so the distance along it is longer.

Concept: A point from its distance and direction cosines
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsDirection cosines of a line

Practise this chapter →

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

Practise this chapter →

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

A bead on the rod is 4.5 m above the floor.

Question 17

Explanation