TS EAMCET · Maths · Three Dimensional Geometry
If the harmonic conjugate of \(\mathrm{P}(2,3,4)\) with respect to the line segment joining the points \(\mathrm{A}(3,-2,2)\) and \(\mathrm{B}(6,-17,-4)\) is \(\mathrm{Q}(\alpha, \beta, \gamma)\), then \(\alpha+\beta+\gamma=\)
- A \(-\frac{2}{5}\)
- B \(-\frac{3}{5}\)
- C \(\frac{7}{5}\)
- D \(\frac{8}{5}\)
Answer & Solution
Correct Answer
(B) \(-\frac{3}{5}\)
Step-by-step Solution
Detailed explanation
Let \(P(2,3,4)\) divides \(A(3,-2,2) 7\) B \((6,-17,-4)\) in the ratio \(\mathrm{k}: 1\) then \(2=\frac{6 k+3}{k+1} \Rightarrow k=-\frac{1}{4}\) Harmonic conjugate Q divides in the ratio \(k: 1\) i.e; \(\frac{1}{4}: 1\)…
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