If \(\mathrm{A}(-4,5, \mathrm{P}), \mathrm{B}(3,1,4)\) and \(\mathrm{C}(-2,0, \mathrm{q})\) are the vertices of a triangle \(A B C\) and \(G(r, q, 1)\) is its centroid, then the value of \(2 p+q-r\) is equal to

\(\mathrm{A}(-4,5, \mathrm{p}), \mathrm{B}(3,1,4)\) and \(\mathrm{C}(-2,0, \mathrm{q})\) are vertices of triangle \(A B C\)
\(\therefore \quad\) Centroid
\(\equiv\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{\mathrm{z}_1+\mathrm{z}_2+\mathrm{z}_3}{3}\right)\)
\(\Rightarrow(\mathrm{r}, \mathrm{q}, 1) \equiv\left(\frac{-4+3-2}{3}, \frac{5+1+0}{3}, \frac{\mathrm{p}+4+\mathrm{q}}{3}\right)\)
\(\begin{aligned}
& \Rightarrow \mathrm{r}=-1, \mathrm{q}=2, \mathrm{p}+\mathrm{q}+4=3 \\
& \Rightarrow \mathrm{r}=-1, \mathrm{q}=2, \mathrm{p}=-3 \\
& \therefore \quad 2 \mathrm{p}+\mathrm{q}-\mathrm{r}=2(-3)+2+1 \\
& =-6+2+1 \\
& =-3
\end{aligned}\)