What is the distance between the parallel lines x/1 = y/2 = z/2 and (x - 3)/1 = (y - 3)/2 = (z - 3)/2?

Three-Dimensional Geometry · Question 111 of 120

Question 111

HardOriginal question

What is the distance between the parallel lines $\frac{x}{1} = \frac{y}{2} = \frac{z}{2}$ and $\frac{x - 3}{1} = \frac{y - 3}{2} = \frac{z - 3}{2}$ ?

\frac{\sqrt{2}}{3}

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\sqrt{2}

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3 \sqrt{2}

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3 \sqrt{3}

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$\vec{b} \times (\vec{a_2} - \vec{a_1}) = 3\hat{j} - 3\hat{k}$ , of length $3\sqrt{2}$ , and $\lvert \vec{b} \rvert = 3$ .
$d = \frac{3\sqrt{2}}{3} = \sqrt{2}$ .

Worth noting

$3\sqrt{3}$ is the distance between the two given points, $(0, 0, 0)$ and $(3, 3, 3)$ .

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

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