Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Given$A\left(7,-\mathrm{8,1}\right),\mathrm{}B\left(p,q,5\right),C\left(q+1,\mathrm{}5p,0\right)$
And centroid, of$∆ABC$is$G\left(3,-5,r\right)$
then,$\hspace{0.17em}p+q+8=9\hspace{0.17em}\Rightarrow p+q=1$… (1)
and$5p+q-8=-15\hspace{0.17em}\Rightarrow \hspace{0.17em}5p+q=-7$… (2)
and$1+5=3r\Rightarrow r=2$
Solving equation (1) and (2) we get$p=–2$and$q=3$