If A(-4, 5, p),B(3, 1, 4),and C(-2, 0, q) are | vedclass

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(A) Given vertices are $A(-4, 5, p)$,$B(3, 1, 4)$,and $C(-2, 0, q)$.The centroid $G(r, q, 1)$ of a triangle with vertices $(x_1, y_1, z_1)$,$(x_2, y_2

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-$3$

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(A) Given vertices are $A(-4, 5, p)$,$B(3, 1, 4)$,and $C(-2, 0, q)$.The centroid $G(r, q, 1)$ 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 $\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3}\right)$.Equating the coordinates,we have:$r = \frac{-4+3-2}{3} = \frac{-3}{3} = -1$$q = \frac{5+1+0}{3} = \frac{6}{3} = 2$$1 = \frac{p+4+q}{3} \Rightarrow p+4+q = 3$Substituting $q=2$ into the equation: $p+4+2 = 3$ $\Rightarrow p+6 = 3$ $\Rightarrow p = -3$.Now,calculating $2p + q - r$:$2(-3) + 2 - (-1) = -6 + 2 + 1 = -3$.

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

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