JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(A (2, 3, 5), B (- 1, 3, 2)\) and \(C (\lambda, 5, \mu)\) be the vertices of a \(\Delta ABC\). If the median through \(A\) 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
If \(D\) be the mid-point of \(B C,\) then \(D=\left(\frac{\lambda-1}{2}, 4, \frac{\mu+2}{2}\right)\) Direction ratios of \(AD\) are \(\frac{\lambda-5}{2}, 1, \frac{\mu-8}{2}\) Since median \(AD\) is equally inclined with coordinate axes, therefore direction ratios of \(AD\)…
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