Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

The direction ratios of the line joining the points $(7,p,2)$ and $(q,-2,5)$ are $(q-7,-2-p,5-2)=(q-7,-2-p,3)$.

The direction ratios of the line joining the points $(2,-3,5)$ and $(-6,-15,11)$ are $(-6-2,-15-(-3),11-5)=(-8,-12,6)$.

Since the two lines are parallel, their direction ratios are proportional:

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

$\frac{q-7}{-8}=\frac{-2-p}{-12}=\frac{1}{2}$

Equating the terms to $\frac{1}{2}$:

$\frac{q-7}{-8}=\frac{1}{2}\Rightarrow q-7=-4\Rightarrow q=3$

$\frac{-2-p}{-12}=\frac{1}{2}\Rightarrow -2-p=-6\Rightarrow p=4$

Therefore, $p=4$ and $q=3$.

Answer: $p=4,q=3$