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 \(\cos ^{-1}\left(\frac{\alpha}{\beta}\right)=\)
- A \(\cos ^{-1}\left(\frac{-1}{9}\right)\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi}{3}\)
- D \(\cos ^{-1}\left(\frac{2}{5}\right)\)
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…
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