Match each line in List I with how it lies relative to L: r = λ(2 i + j) in List II. | List I | List II | |---|---| | A. r = k + μ(2 i + j) | I. Skew | | B. r = k + μ( i - 2 j) | II. The same line | | C. r = k + μ(2 i + j - k) | III. Parallel and distinct | | D. r = (4 i + 2 j) + μ(-2 i - j) | IV. Meeting at one point |

Match each line in List I with how it lies…

Match each line in List I with how it lies relative to L:

Question 105

MediumOriginal question

Match each line in List I with how it lies relative to $L: \vec{r} = \lambda(2\hat{i} + \hat{j})$ in List II.

List I	List II
A. $\vec{r} = \hat{k} + \mu(2\hat{i} + \hat{j})$	I. Skew
B. $\vec{r} = \hat{k} + \mu(\hat{i} - 2\hat{j})$	II. The same line
C. $\vec{r} = \hat{k} + \mu(2\hat{i} + \hat{j} - \hat{k})$	III. Parallel and distinct
D. $\vec{r} = (4\hat{i} + 2\hat{j}) + \mu(-2\hat{i} - \hat{j})$	IV. Meeting at one point

A-I, B-III, C-IV, D-IICorrect answerYour answerA-III, B-I, C-II, D-IVCorrect answerYour answerA-I, B-III, C-II, D-IVCorrect answerYour answerA-III, B-I, C-IV, D-IICorrect answerYour answer

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CorrectNot quiteAnswer D

Correct answer: D

A has the direction of $L$ , and $(0, 0, 1)$ is not on $L$ : parallel and distinct. D has direction $-(2\hat{i} + \hat{j})$ and passes through $(4, 2, 0)$ , a point of $L$ : the same line.
B and C are not parallel to $L$ . With $\vec{a}_2 - \vec{a}_1 = \hat{k}$ , $\hat{k} \cdot (\vec{b}_1 \times \vec{b}_2)$ is $-5$ for B, so B is skew, and 0 for C, which meets $L$ at $(2, 1, 0)$ .

Concept: Classifying a pair of lines
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsSkew lines and the shortest distance

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

Practise this chapter →

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

Match each line in List I with how it lies relative to L:

Question 105

Explanation