AP EAMCET · Maths · Three Dimensional Geometry
Let \(\mathrm{A}(2,3,5), \mathrm{B}(-1,3,2), \mathrm{C}(\lambda, 5, \mu)\) be the vertices of \(\triangle \mathrm{ABC}\). If the median through the vertex A is equally inclined to the coordinate axes, then
- A \(5 \lambda-8 \mu=0\)
- B \(8 \lambda-5 \mu=0\)
- C \(10 \lambda-7 \mu=0\)
- D \(7 \lambda-10 \mu=0\)
Answer & Solution
Correct Answer
(C) \(10 \lambda-7 \mu=0\)
Step-by-step Solution
Detailed explanation
Let D be the midpoint of BC. \(D = \left(\frac{-1+\lambda}{2}, \frac{3+5}{2}, \frac{2+\mu}{2}\right) = \left(\frac{\lambda-1}{2}, 4, \frac{\mu+2}{2}\right)\) Direction ratios of median AD (A(2,3,5)): \(l = \frac{\lambda-1}{2} - 2 = \frac{\lambda-5}{2}\) \(m = 4 - 3 = 1\)…
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