For which p and q are the lines (x - 1)/2 = (y + 1)/p = (z - 2)/3 and (x + 3)/q = (y - 2)/(-6) = z/9 parallel?

Three-Dimensional Geometry · Question 73 of 120

Question 73

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For which $p$ and $q$ are the lines $\frac{x - 1}{2} = \frac{y + 1}{p} = \frac{z - 2}{3}$ and $\frac{x + 3}{q} = \frac{y - 2}{-6} = \frac{z}{9}$ parallel?

p = -2, q = 6

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p = -18, q = 6

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p = 2, q = 6

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p = -2, q = \frac{2}{3}

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CorrectNot quiteAnswer A

Correct answer: A

Parallel lines have proportional direction ratios: $\frac{q}{2} = \frac{-6}{p} = \frac{9}{3} = 3$ .
So $q = 6$ and $p = -2$ .

Worth noting

$p = -18$ multiplies $-6$ by 3 where it should divide.

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

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