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AP EAMCET · Maths · Three Dimensional Geometry

If a point \(\mathrm{R}(4, \mathrm{y}, \mathrm{z})\) lies on the line joining the points \(P(2,-3,4)\) and \(Q(8,0,10)\), then distance of \(R\) from origin is

  1. A \(2 \sqrt{14}\)
  2. B \(6\)
  3. C \(\sqrt{53}\)
  4. D \(2 \sqrt{21}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(2 \sqrt{14}\)

Step-by-step Solution

Detailed explanation

Equation of line joining point \(\mathrm{P}\) and \(\mathrm{Q}\) : \(\frac{x^{\prime}-2}{8-2}=\frac{y^{\prime}+3}{0+3}=\frac{z^{\prime}-4}{10-4}=\lambda(\) say \()\) \(\Rightarrow \quad x^{\prime}=6 \lambda+2, y^{\prime}=3 \lambda-3, z^{\prime}=6 \lambda+4\) \(\because \quad\)…