A second rod runs from P to a point R on the…

A second rod runs from P to a point R on the x-axis and is perpendicular to the first rod.

Question 25

HardOriginal 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 second rod runs from $P$ to a point $R$ on the $x$ -axis and is perpendicular to the first rod. How far is $R$ from $O$ ?

6 mCorrect answerYour answer

\frac{85}{6}

mCorrect answerYour answer

\frac{113}{6}

mCorrect answerYour answer

\frac{121}{6}

mCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

With $R(r, 0, 0)$ , $PR$ has direction ratios $r - 6, -2, -9$ , and it must be perpendicular to $6, 2, 9$ .
$6(r - 6) - 4 - 81 = 0$ , so $6r = 121$ and $OR = \frac{121}{6}$ m.

Worth noting

6 m stops at the $x$ -coordinate of $P$ ; then $PR$ is not perpendicular to $OP$ .

Concept: Perpendicular lines
Typical timeTypical: 150 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 second rod runs from P to a point R on the x-axis and is perpendicular to the first rod.

Question 25

Explanation