Question

If the origin is the centroid of the triangle $PQR$ with vertices $P(2a,2,6),Q(-4,3b,-10)$ and $R(8,14,2c),$ then find the values of $a,b$ and $c$

Answer 1

The coordinates of the centroid of $△PQR$
$=(\frac{2a-4-8}{3},\frac{2+3b+14}{3},\frac{6-10+2c}{3})=(\frac{2a+4}{3},\frac{3b+16}{3},\frac{2c-4}{3})$
It is given that origin is the centroid of $△PQR$
$\therefore$ $(0,0,0)=(\frac{2a+4}{3},\frac{3b+16}{3},\frac{2c-4}{3})$
$\Rightarrow \frac{2a+4}{3}=0,\frac{3b+16}{3}=0\text{and}\frac{2c-4}{3}=0$
$\Rightarrow a=-2,b=-\frac{16}{3}$ and $c=2$