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A line with dr’s $(2, 7, - 5)$ is drawn to intersect the lines $\frac{x - 5}{3} = \frac{y - 7}{- 1} = \frac{z + 2}{1}$ and $\frac{x + 3}{- 3} = \frac{y - 3}{2} = \frac{z - 6}{4}$ at P and Q respectively, then length of PQ is.

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$\sqrt{74}$

$\sqrt{48}$

$\sqrt{77}$

$\sqrt{78}$

answer is D.

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Detailed Solution

$P (5 + 3 t, 7 - t, - 2 + t)$ , $Q (- 3 - 3 λ, 3 + 2 λ, 6 + 4 λ)$

Dr’s of PQ =

$(8 + 3 t + 3 λ, 4 - t - 2 λ, t - 4 λ - 8)$

$= (2, 7, - 5)$

$∴ t = λ = - 1$

$P (2, 8, - 3) Q (0, 1, 2) \Rightarrow P Q = \sqrt{78}$

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