AP EAMCET · Maths · Three Dimensional Geometry
The harmonic conjugate of \(P(-9,12,-15)\) with respect to the line segment \(A B\), where \(A=(1,-2,3)\) and \(B=(-4,5,-6)\) is
- A \(\left(-\frac{2}{3}, \frac{1}{3}, 0\right)\)
- B \((6,-9,12)\)
- C \(\left(-\frac{7}{3}, \frac{8}{3},-3\right)\)
- D \(\left(\frac{7}{3},-\frac{8}{3}, \frac{9}{3}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(-\frac{7}{3}, \frac{8}{3},-3\right)\)
Step-by-step Solution
Detailed explanation
Let point \(P(-9,12,-15)\) divides the line joining \(A(1,-2,3)\) and \(B(-4,5,-6)\) in ratio \(\lambda: 1\). Then, \(\quad-9=\frac{-4 \lambda+1}{\lambda+1}, \lambda=-2\) So, harmonic conjugate of point ' \(P\) ' with respect to the line segment \(A B\) will divides the line…
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