Which describes the lines (x - 1)/2 = (y + 2)/1 = (z - 3)/(-1) and (x + 1)/1 = (y - 1)/(-1) = (z - 2)/2?

Question 102

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Which describes the lines $\frac{x - 1}{2} = \frac{y + 2}{1} = \frac{z - 3}{-1}$ and $\frac{x + 1}{1} = \frac{y - 1}{-1} = \frac{z - 2}{2}$ ?

SkewCorrect answerYour answerMeeting at one pointCorrect answerYour answerParallel and distinctCorrect answerYour answerThe same lineCorrect answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

$2, 1, -1$ and $1, -1, 2$ are not proportional, so the lines are not parallel.
$(\vec{a}_2 - \vec{a}_1) \cdot (\vec{b}_1 \times \vec{b}_2) = (-2\hat{i} + 3\hat{j} - \hat{k}) \cdot (\hat{i} - 5\hat{j} - 3\hat{k}) = -14 \ne 0$ : they do not meet either, so they are skew.

Worth noting

Lines that are not parallel need not meet: in space they can be skew.

Concept: Classifying a pair of lines
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsSkew lines and the shortest distance

Practise this chapter →

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

Which describes the lines x−12=y+21=z−3−1\frac{x - 1}{2} = \frac{y + 2}{1} = \frac{z - 3}{-1}2x−1​=1y+2​=−1z−3​ and x+11=y−1−1=z−22\frac{x + 1}{1} = \frac{y - 1}{-1} = \frac{z - 2}{2}1x+1​=−1y−1​=2z−2​?

Explanation

Which describes the lines $\frac{x - 1}{2} = \frac{y + 2}{1} = \frac{z - 3}{-1}$ and $\frac{x + 1}{1} = \frac{y - 1}{-1} = \frac{z - 2}{2}$ ?