If a triangle ABC with two vertices A(5,4,6) | vedclass

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(C) Let the coordinates of the third vertex $C$ be $(x, y, z)$.Given vertices are $A(5, 4, 6)$ and $B(1, -1, 3)$.The centroid $G$ of a triangle with v

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$(4,3,2)$

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(C) Let the coordinates of the third vertex $C$ be $(x, y, z)$.Given vertices are $A(5, 4, 6)$ and $B(1, -1, 3)$.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 centroid $G = \left(\frac{10}{3}, 2, \frac{11}{3}\right)$.Equating the coordinates:$\frac{5+1+x}{3} = \frac{10}{3} \Rightarrow 6+x = 10 \Rightarrow x = 4$.$\frac{4-1+y}{3} = 2 \Rightarrow 3+y = 6 \Rightarrow y = 3$.$\frac{6+3+z}{3} = \frac{11}{3} \Rightarrow 9+z = 11 \Rightarrow z = 2$.Therefore, the third vertex $C$ is $(4, 3, 2)$.

If a triangle $ABC$ with two vertices $A(5,4,6)$ and $B(1,-1,3)$ has its centroid at $\left(\frac{10}{3}, 2, \frac{11}{3}\right)$, then the third vertex $C$ is

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