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TS EAMCET · Maths · Three Dimensional Geometry

The direction ratios of the line bisecting the angle between the \(x\)-axis and the line having direction ratios \((3,-1,5)\) are

  1. A \(\frac{3}{\sqrt{7}},-\frac{1}{\sqrt{7}}, \frac{5}{\sqrt{7}}\)
  2. B \(\frac{3+\sqrt{35}}{\sqrt{7}}, \frac{1}{\sqrt{5}},-\frac{5}{\sqrt{5}}\)
  3. C \(\frac{\sqrt{35}-3}{\sqrt{5}}, \frac{1}{\sqrt{5}},-\sqrt{5}\)
  4. D \(\frac{\sqrt{35}-3}{\sqrt{35}}, \frac{1}{\sqrt{7}}, \frac{5}{\sqrt{7}}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{\sqrt{35}-3}{\sqrt{5}}, \frac{1}{\sqrt{5}},-\sqrt{5}\)

Step-by-step Solution

Detailed explanation

Let \(\vec{a}\) be the direction vector for the x-axis and \(\vec{b}\) be the direction vector for the second line. \(\vec{a} = (1,0,0)\), \(|\vec{a}| = \sqrt{1^2} = 1\) \(\vec{b} = (3,-1,5)\), \(|\vec{b}| = \sqrt{3^2 + (-1)^2 + 5^2} = \sqrt{9+1+25} = \sqrt{35}\) Unit vectors…