If A (1, 2, 3), B (2, -3, 1), C (3, 2, -1) are three vertices of a tetrahedron ABCD and G52,32,94 is its centroid then the point which divides GD¯ in the ratio 1:2 is

G=A+B+C+D4 ⇒ D=4G−A−B−C D=[4,5,6] p=1(D)+2(G)1+2=14,5,6+252,32,943=3,83,72

If A (1, 2, 3), B (2, -3, 1), C (3, 2, -1) are three vertices of a tetrahedron ABCD and G52,32,94 is its centroid then the point which divides GD¯ in the ratio 1:2 is

G=A+B+C+D4 ⇒ D=4G−A−B−C D=[4,5,6] p=1(D)+2(G)1+2=14,5,6+252,32,943=3,83,72

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If A (1, 2, 3), B (2, -3, 1), C (3, 2, -1) are three vertices of a tetrahedron ABCD and $G (\frac{5}{2}, \frac{3}{2}, \frac{9}{4})$ is its centroid then the point which divides $\bar{G D}$ in the ratio 1:2 is

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$(3, \frac{8}{3}, \frac{7}{2})$

$(\frac{1}{3}, \frac{2}{3}, 1)$

(6, 1, 3)

$(3, \frac{8}{3}, 3)$

answer is D.

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Detailed Solution

$G = \frac{A + B + C + D}{4} \Rightarrow D = 4 G - A - B - C$
$\begin{aligned} D = [4, 5, 6] \\ p = \frac{1 (D) + 2 (G)}{1 + 2} \end{aligned}$
$= \frac{1 (4, 5, 6) + 2 (\frac{5}{2}, \frac{3}{2}, \frac{9}{4})}{3} = (3, \frac{8}{3}, \frac{7}{2})$

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If A (1, 2, 3), B (2, -3, 1), C (3, 2, -1) are three vertices of a tetrahedron ABCD and G52,32,94 is its centroid then the point which divides GD¯ in the ratio 1:2 is

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If A (1, 2, 3), B (2, -3, 1), C (3, 2, -1) are three vertices of a tetrahedron ABCD and $G (\frac{5}{2}, \frac{3}{2}, \frac{9}{4})$ is its centroid then the point which divides $\bar{G D}$ in the ratio 1:2 is