AP EAMCET · Maths · Three Dimensional Geometry
If \(\mathrm{A}(2,-1,1), \mathrm{B}(2,5,1)\) and \(\mathrm{C}(0,-2,3)\) are the vertices of a triangle. If D is the point of intersection of the side BC and the internal angular bisector of angle A, then \(\mathrm{AD}=\)
- A \(\frac{5}{\sqrt{7}}\)
- B \(\frac{3}{\sqrt{2}}\)
- C \(\frac{\sqrt{3}}{2}\)
- D \(\frac{4}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(D) \(\frac{4}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{AB} = \sqrt{(2-2)^2 + (5-(-1))^2 + (1-1)^2} = \sqrt{0^2 + 6^2 + 0^2} = 6\) \(\mathrm{AC} = \sqrt{(0-2)^2 + (-2-(-1))^2 + (3-1)^2} = \sqrt{(-2)^2 + (-1)^2 + 2^2} = 3\) \(\frac{\mathrm{BD}}{\mathrm{DC}} = \frac{\mathrm{AB}}{\mathrm{AC}} = \frac{6}{3} = 2:1\)…
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