Question

If the line joining the points $(k,1,2),(3,4,6)$ is parallel to the line joining the points $(-4,3,-6),(5,12,l)$ then $(k,l)$ is:

• A. $(-2,7)$
• B. $(0,6)$
• C. $(0,-6)$
• D. $(2,-7)$

Answer 1

The correct option is B $(0,6)$

DR's of line joining $(k,1,2),(3,4,6)$ is $(3-k,3,4)=(a_1,b_1,c_1)$
DR's of line joining $(-4,3,-6),(5,12,l)$ is $(9,9,l+6)=(a_2,b_2,c_2)$
Since two lines are parallel,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\frac{3-k}{9}=\frac{3}{9}=\frac{4}{l+6}$
So, $k=0,l=6$
Therefore, $(k,l)=(0,6)$