If the line joining the points \((k, 3,4),(4,7,8)\) is parallel to the line joining the points \((-1,-2,1)…
If the line joining the points \((k, 3,4),(4,7,8)\) is parallel to the line joining the points \((-1,-2,1),(1,2, l)\), then \(k+l=\)
2
5
7
-3
Solution
The direction ratios of line joining points \((k, 3,4)\) and \((4,7,8)\) is \(k-4,-4,-4\) and similarly the direction ratios of line joining points \((-1,-2,1)\) and \((1,2,1)\) is \(-2,-4,1-1\).
\(\therefore\) Both line segments are parallel, so
\(\begin{array}{llll}
& \frac{k-4}{-2} & =\frac{-4}{-4}=\frac{-4}{1-l} \Rightarrow k=2 \text { and } l=5 \\
\therefore & k+l & =7
\end{array}\)