If $A \equiv(5,1, p), B \equiv(1, q, p)$ and $C \equiv(1,-2,3)$ are vertices of the triangle and $G \equiv\left(r,-\frac{4}{3}, \frac{1}{3}\right)$ is its centroid, then the values of $p, q, r$ are respectively

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Aicharya · Accepted Answer

$\begin{aligned} & \left(r, \frac{-4}{3}, \frac{1}{3}ight) \equiv\left(\frac{5+1+1}{3}, \frac{1+q-2}{3}, \frac{p+p+3}{3}ight) \ & \Rightarrow r=\frac{7}{3}, \frac{-4}{3}=\frac{q-1}{3}, \frac{1}{3}=\frac{2 p+3}{3} \ & \Rightarrow p=-1, q=-3, r=\frac{7}{3}\end{aligned}$

If $A \equiv(5,1, p), B \equiv(1, q, p)$ and $C \equiv(1,-2,3)$ are vertices of the triangle and $G…

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