If the line \frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4} \textrm{ }\textrm{ } and \textrm{ }\textrm{ } \frac{x - 3}{1} = \frac{y - k}{2} = \frac{z}{1} intersect, then k is equal to :

Engineering

Mathematics

Shortest Distance Between Two Lines

Question

If the line $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4} and \frac{x - 3}{1} = \frac{y - k}{2} = \frac{z}{1}$ intersect, then k is equal to :

$\frac{2}{9}$

–1

$\frac{9}{2}$

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If the line $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4} and \frac{x - 3}{1} = \frac{y - k}{2} = \frac{z}{1}$ intersect, then $| \begin{matrix} 3 - 1 & k + 1 & 0 - 1 \\ 2 & 3 & 4 \\ 1 & 2 & 1 \end{matrix} | = 0$

$\Rightarrow$ 2 (3 – 8) – (k + 1) (2 – 4) – 1 (4 – 3) = 0

$\Rightarrow$ – 10 + 2k + 2 – 1 = 0

$\Rightarrow 2 k = 9 \Rightarrow k = \frac{9}{2}$ .

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