TS EAMCET · Maths · Three Dimensional Geometry
Let \(A=(1,2,0), B=(2,0,-1), C=(0,-2,3)\) and \(D=(-1,2,-3)\) be four points in the space. Let \(\mathrm{G}_1\) be the centroid of triangle \(A B C\) and \(G_2\) be the centroid of tetrahedron ABCD. If \(P\) divides \(G_1 G_2\) in the ratio \(4: 3\) internally then \(\mathrm{P}=\)
- A \(\left(\frac{5}{7}, \frac{2}{7}, \frac{1}{7}\right)\)
- B \(\left(\frac{1}{7}, \frac{2}{7}, \frac{3}{7}\right)\)
- C \(\left(\frac{4}{7}, \frac{-2}{7}, \frac{1}{7}\right)\)
- D \(\left(\frac{1}{7}, \frac{-3}{7}, \frac{5}{7}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{5}{7}, \frac{2}{7}, \frac{1}{7}\right)\)
Step-by-step Solution
Detailed explanation
Given points are \(\mathrm{A}=(1,2,0), \mathrm{B}=(2,0,-1)\), \(\mathrm{C}=(0,-2,3)\) and \(\mathrm{D}=(-1,2,-3)\) Here \(\mathrm{G}_1=(1,0,2 / 3)\) and \(\mathrm{G}_2=(1 / 2,1 / 2,-1 / 4)\) Now \(P\) divides \(G_1 G_2\) in the ratio \(4: 3\) internally So,…
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