What is the shortest distance between the lines x/1 = (y - 1)/1 = (z - 2)/1 and (x - 1)/1 = y/(-1) = z/2?

Question 112

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What is the shortest distance between the lines $\frac{x}{1} = \frac{y - 1}{1} = \frac{z - 2}{1}$ and $\frac{x - 1}{1} = \frac{y}{-1} = \frac{z}{2}$ ?

\frac{4}{7}

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\frac{2 \sqrt{14}}{7}

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\frac{4 \sqrt{14}}{7}

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8

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Points $(0, 1, 2)$ , $(1, 0, 0)$ ; directions $1, 1, 1$ and $1, -1, 2$ ; $\vec{b_1} \times \vec{b_2} = 3\hat{i} - \hat{j} - 2\hat{k}$ .
$(\vec{a_2} - \vec{a_1}) \cdot (\vec{b_1} \times \vec{b_2}) = 3 + 1 + 4 = 8$ , so $d = \frac{8}{\sqrt{14}}$ .

Worth noting

$\frac{4}{7} = \frac{8}{14}$ divides by $\lvert \vec{b_1} \times \vec{b_2} \rvert^{2}$ instead of its length.

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