TS EAMCET · Maths · Three Dimensional Geometry
\(A(1,2,3), B(2,3,1)\) and \(C(3,1,2)\) are three points. If the point \(\mathrm{P}\) divides \(\mathrm{AB}\) in the ratio \(1: 2\) and the point \(\mathrm{Q}\) divides \(\mathrm{BC}\) in the ratio \(-2: 3\), then the distance between \(P\) and \(Q\) is
- A \(\sqrt{312}\)
- B 13
- C \(\frac{2}{3} \sqrt{78}\)
- D 25
Answer & Solution
Correct Answer
(C) \(\frac{2}{3} \sqrt{78}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & x=\frac{2+2}{3}, y=\frac{3+4}{3}, z=\frac{1+6}{3} \\ & P(x, y, z)=\left(\frac{4}{3}, \frac{7}{3}, \frac{7}{3}\right) \\ & \text {. } \begin{array}{ll} & -2,1 \\ B & Q \end{array} \\ & (2,3,1) \quad(\alpha, \beta, \gamma) \quad(3,1,2) \\ & \alpha=\frac{-6+6}{1},…
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