If A equiv (5, 1, p),B equiv (1, q, p),and C | vedclass

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(D) The centroid $G$ of a triangle with vertices $(x_1, y_1, z_1)$,$(x_2, y_2, z_2)$,and $(x_3, y_3, z_3)$ is given by $\left(\frac{x_1+x_2+x_3}{3}, \

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$-1, -3, \frac{7}{3}$

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(D) The centroid $G$ of a triangle with vertices $(x_1, y_1, z_1)$,$(x_2, y_2, z_2)$,and $(x_3, y_3, z_3)$ is given by $\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3}\right)$.Given $G = (r, -\frac{4}{3}, \frac{1}{3})$,we equate the coordinates:$r = \frac{5+1+1}{3} = \frac{7}{3}$$-\frac{4}{3} = \frac{1+q-2}{3}$ $\Rightarrow -4 = q-1$ $\Rightarrow q = -3$$\frac{1}{3} = \frac{p+p+3}{3}$ $\Rightarrow 1 = 2p+3$ $\Rightarrow 2p = -2$ $\Rightarrow p = -1$Thus,the values are $p = -1, q = -3, r = \frac{7}{3}$.

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

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