Read the two statements and choose the correct option. I. The distance between the parallel lines r = λ( i + j + k) and r = 2 i + μ( i + j + k) is (2√(6))/3. II. The lines r = (2 i + k) + λ( i - j) and r = ( i + 2 j + 2 k) + μ( j + k) meet at (1, 1, 1).

Question 103

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Read the two statements and choose the correct option.
I. The distance between the parallel lines $\vec{r} = \lambda(\hat{i} + \hat{j} + \hat{k})$ and $\vec{r} = 2\hat{i} + \mu(\hat{i} + \hat{j} + \hat{k})$ is $\frac{2\sqrt{6}}{3}$ .
II. The lines $\vec{r} = (2\hat{i} + \hat{k}) + \lambda(\hat{i} - \hat{j})$ and $\vec{r} = (\hat{i} + 2\hat{j} + 2\hat{k}) + \mu(\hat{j} + \hat{k})$ meet at $(1, 1, 1)$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

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CorrectNot quiteAnswer C

Correct answer: C

I: $(\hat{i} + \hat{j} + \hat{k}) \times 2\hat{i} = 2\hat{j} - 2\hat{k}$ , of length $2\sqrt{2}$ ; divided by $\sqrt{3}$ it gives $\frac{2\sqrt{6}}{3}$ . True.
II: $\lambda = -1$ gives $(1, 1, 1)$ on the first line and $\mu = -1$ gives $(1, 1, 1)$ on the second. True.

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