AP EAMCET · Maths · Three Dimensional Geometry
If \(\mathrm{Q}(\alpha, \beta, \gamma)\) is the harmonic conjugate of the point \(\mathrm{P}(0,-7,1)\) with respect to the line segment joining the points \((2,-5,3)\) and \((-1,-8,0)\), then \(\alpha-\beta+\gamma=\)
- A 4
- B 3
- C 2
- D 1
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
\(A=(2,-5,3)\), \(B=(-1,-8,0)\), \(P=(0,-7,1)\) Let P divide AB in ratio \(\lambda:1\): \(\frac{2+\lambda(-1)}{1+\lambda} = 0 \Rightarrow \lambda=2\) Q divides AB in ratio \(-\lambda:1\): \(Q = \frac{1 \cdot A + (-\lambda) \cdot B}{1-\lambda} = \frac{A-2B}{-1} = 2B-A\)…
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