If two vertices of a triangle are A(3,1,4) an | vedclass

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(B) Let the coordinates of the third vertex $C$ be $(x, y, z)$.Since $G$ is the centroid of $	riangle ABC$,the coordinates of $G$ are given by the fo

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$(-2,0,2)$

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(B) Let the coordinates of the third vertex $C$ be $(x, y, z)$.Since $G$ is the centroid of $	riangle ABC$,the coordinates of $G$ are given by the formula:$G = \left( \frac{x_A + x_B + x_C}{3}, \frac{y_A + y_B + y_C}{3}, \frac{z_A + z_B + z_C}{3} ight)$Given $A(3, 1, 4)$,$B(-4, 5, -3)$,and $G(-1, 2, 1)$:$-1 = \frac{3 - 4 + x}{3} \implies -3 = -1 + x \implies x = -2$$2 = \frac{1 + 5 + y}{3} \implies 6 = 6 + y \implies y = 0$$1 = \frac{4 - 3 + z}{3} \implies 3 = 1 + z \implies z = 2$Therefore,the third vertex $C$ is $(-2, 0, 2)$.

If two vertices of a triangle are $A(3,1,4)$ and $B(-4,5,-3)$ and the centroid of the triangle is $G(-1,2,1)$,then the third vertex $C$ of the triangle is

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