AP EAMCET · Maths · Three Dimensional Geometry
\(A(3,2,-1), B(4,1,1), C(6,2,5)\) and \(D(3,3,3)\) are four points. \(G_1, G_2, G_3\) and \(G_4\) respectively are the centroids of the triangles \(\triangle B C D, \triangle C D A\), \(\triangle D A B\) and \(\triangle A B C\). The point of concurrence of the lines \(A G_1, B G_2, C G_3\) and \(D G_4\) is
- A (4, 2, 2)
- B (2, 4, 2)
- C (2, 2, 4)
- D (2, 2, 2)
Answer & Solution
Correct Answer
(A) (4, 2, 2)
Step-by-step Solution
Detailed explanation
Given points, \(A(3,2,-1), B(4,1,1), C(6,2,5)\) and \(D(3,3,3)\), So, \(G_1\) is centroid of triangle BCD, \(G_1 \equiv\left(\frac{13}{3}, \frac{6}{3}, \frac{9}{3}\right)\) \(G_2\) is centroid of triangle CDA \(G_2 \equiv\left(\frac{12}{3}, \frac{7}{3}, \frac{7}{3}\right)\)…
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