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If the origin is the centroid of the triangle whose vertices are $\mathrm{A}(2, \mathrm{p},-3)$, $\mathrm{B}(\mathrm{q},-2,5)$ and $\mathrm{C}(-5,1, \mathrm{r})$, then
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Verified Answer
The correct answer is:
$p=1, \quad q=3, \quad r=-2$
Origin is centroid of $\Delta \mathrm{ABC}$.
$$
\begin{array}{l}
\therefore \frac{2+q-5}{3}=0 \Rightarrow-3+q=0 \Rightarrow q=3 \\
\therefore \frac{p-2+1}{3}=0 \Rightarrow p-1=0 \Rightarrow p=1 \\
\therefore \frac{-3+5+r}{3}=0 \Rightarrow 2+r=0 \Rightarrow r=-2
\end{array}
$$
$$
\begin{array}{l}
\therefore \frac{2+q-5}{3}=0 \Rightarrow-3+q=0 \Rightarrow q=3 \\
\therefore \frac{p-2+1}{3}=0 \Rightarrow p-1=0 \Rightarrow p=1 \\
\therefore \frac{-3+5+r}{3}=0 \Rightarrow 2+r=0 \Rightarrow r=-2
\end{array}
$$
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