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AP EAMCET · Maths · Straight Lines

\(A(2,3,5), B(\alpha, 3,3)\) and \(C(7,5, \beta)\) are the vertices of a triangle. If the median through \(A\) is equally inclined with the co-ordinate axes, then \(\cos ^{-1}\left(\frac{\alpha}{\beta}\right)=\)

  1. A \(\cos ^{-1}\left(\frac{-1}{9}\right)\)
  2. B \(\frac{\pi}{2}\)
  3. C \(\frac{\pi}{3}\)
  4. D \(\cos ^{-1}\left(\frac{2}{5}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\cos ^{-1}\left(\frac{-1}{9}\right)\)

Step-by-step Solution

Detailed explanation

Given, points \(A(2,3,5), B(\alpha, 3,3)\) and \(C(7,5, \beta)\) \(\therefore\) Mid-point of \(B C\) is \(D\left(\frac{\alpha+7}{2}, 4, \frac{3+\beta}{2}\right)\) \(\because\) Direction ratios of line joining points \(A(2,3,5)\) and…