ExamBro
ExamBro
AP EAMCET · Maths · Straight Lines

\(A(3,2,-1), B(4,1,1), C(6,2,5)\) are three points. If \(D, E, F\) are three points which divide \(B C\), \(C A, A B\) respectively in the same ratio \(2: 1\), then the centroid of \(\triangle D E F\) is

  1. A \(\left(\frac{13}{3}, \frac{5}{3}, \frac{5}{3}\right)\)
  2. B \((13,5,5)\)
  3. C \((4,2,1)\)
  4. D \(\left(\frac{11}{3}, \frac{4}{3}, \frac{1}{3}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\left(\frac{13}{3}, \frac{5}{3}, \frac{5}{3}\right)\)

Step-by-step Solution

Detailed explanation

Here, \(D=\left(\frac{2 \times 6+4 \times 1}{3}, \frac{2 \times 2+1 \times 1}{3}, \frac{2 \times 5+1 \times 1}{3}\right)\) \(=\left(\frac{16}{3}, \frac{5}{3}, \frac{11}{3}\right)\) Similarly,…