Assertion (A): The lines $\vec{r} = \hat{i} + \lambda(\hat{i} + \hat{j})$ and $\vec{r} = \hat{j} + \mu(\hat{i} + \hat{k})$ intersect.
Reason (R): Two lines intersect exactly when the shortest distance between them is 0.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

A is false: $(\vec{a}_2 - \vec{a}_1) \cdot (\vec{b}_1 \times \vec{b}_2) = (-\hat{i} + \hat{j}) \cdot (\hat{i} - \hat{j} - \hat{k}) = -2 \ne 0$ , so the distance is not 0.
R is true for non-parallel lines, which these are.

Concept: Testing whether two lines meet
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.

Assertion (A): The lines r⃗=i^+λ(i^+j^)\vec{r} = \hat{i} + \lambda(\hat{i} + \hat{j})r=i^+λ(i^+j^​) and r⃗=j^+μ(i^+k^)\vec{r} = \hat{j} + \mu(\hat{i} + \hat{k})r=j^​+μ(i^+k^) intersect.Reason (R): Two lines intersect exactly when the shortest distance between them is 0.

Explanation

Assertion (A): The lines $\vec{r} = \hat{i} + \lambda(\hat{i} + \hat{j})$ and $\vec{r} = \hat{j} + \mu(\hat{i} + \hat{k})$ intersect.
Reason (R): Two lines intersect exactly when the shortest distance between them is 0.