Question

If the line joining the points $(k,2,3),(1,1,2)$ is parallel to the line joining the points $(5,4,-1),(3,2,-3)$ then the value of $k$ is:

Answer 1

Let points $A(k,2,3),B(1,1,2)$ and $C(5,4,-1),D(3,2,-3)$
D.R's of $\overrightarrow{AB}=(1-k,-1,-1)$
D.R's of $\overrightarrow{CD}=(-2,-2,-2)=(1,1,1)$
For lines to be parallel,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\Rightarrow \frac{1-k}{1}=\frac{-1}{1}=\frac{-1}{1}\Rightarrow k=2$