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AP EAMCET · Maths · Three Dimensional Geometry

Let \(\mathrm{P}(\alpha, 4,7)\) and \(\mathrm{Q}(3, \beta, 8)\) are two points. If YZ - plane divides the join of the points \(P\) and \(Q\) in the ratio 2:3 and ZX - plane divides the join of P and Q in the ratio \(4: 5\). then length of line segment PQ is

  1. A \(\sqrt{107}\)
  2. B \(\sqrt{27}\)
  3. C \(\sqrt{83}\)
  4. D \(\sqrt{97}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\sqrt{107}\)

Step-by-step Solution

Detailed explanation

Given, \(P(\alpha, 4,7)\) and \(Q(3, \beta, 8)\) Since, YZ - plane divide the line joining the point P and Q in ratio \(=2: 3\) So, its x -coordinate is zero \(\Rightarrow \frac{3 \alpha+2.3}{2+3}=0 \Rightarrow \alpha=-2\) and ZX -plane divide the line joining the point \(P\)…