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If the lines ( x - 1 ) /(2 ) = ( y...

If the lines ` ( x - 1 ) /(2 ) = ( y + 1) / ( 3 ) = ( z - 1 ) / ( 4 ) and ( x - 3 ) / ( 1 ) = ( y - k ) / ( 2 ) = (z) / ( 1 ) ` intersect, then find the value of k.

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To find the value of \( k \) such that the given lines intersect, we can use the condition for the intersection of two lines in space. The lines are given in symmetric form. The lines are: 1. \( \frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4} \) 2. \( \frac{x - 3}{1} = \frac{y - k}{2} = \frac{z}{1} \) Let’s denote the first line as \( L_1 \) and the second line as \( L_2 \). ...
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