Question

The values of $p$ and $q$ so that the line joining the points $(7,p,2)$ and $(q,-2,5)$ may be parallel to the line joining the points $(2,-3,5)$ and $(-6,-15,11)$ are

• A. $p=4,q=-3$
• B. $p=4,q=3$
• C. $p=-4,q=3$
• D. $p=-4,q=-3$

Answer 1

The correct option is B $p=4,q=3$

DR of the line through $(7,p,2)$ and $(q,-2,5)=(q-7,-2-p,5-2)$

DR of the line through $(2,-3,5)$ and $(-6,-15,11)=(-6-2,-15+3,11-5)=(-8,-12,6)$

Since the lines are parallel to each other,

DRs must be in same ratio.

$\therefore \frac{q-7}{-8}=\frac{-2-p}{-12}=\frac{3}{6}$

$\therefore \frac{q-7}{-8}=\frac{3}{6}$

$\Rightarrow =q-7=-4$

$\therefore q=3$

And, $\frac{-2-p}{-12}=\frac{1}{2}$

$\Rightarrow -2-p=-6$

$p=4$

Option B is correct