AP EAMCET · Maths · Three Dimensional Geometry
In \(\triangle \mathrm{ABC}\), if the midpoints of the sides \(\mathrm{AB}, \mathrm{BC}\) and \(\mathrm{CA}\) are respectively \((l, 0,0),(0, \mathrm{~m}, 0)\) and \((0,0, \mathrm{n})\), then \(\frac{\mathrm{AB}^2+\mathrm{BC}^2+\mathrm{CA}^2}{l^2+\mathrm{m}^2+\mathrm{n}^2}=\)
- A 2
- B 4
- C 8
- D 16
Answer & Solution
Correct Answer
(C) 8
Step-by-step Solution
Detailed explanation
\(\therefore(l, 0,0)\) is mid point of AB. \(\Rightarrow x_1+x_2=2 l ; y_1+y_2=0 ; z_1+z_2=0\) ...(i) \((0, m, 0)\) is mid point of \(\mathrm{BC}\). \(\therefore\left(\frac{x_2+x_3}{2}, \frac{y_2+y_3}{2}, \frac{z_2+z_3}{2}\right)=(0, \mathrm{~m}, 0)\)…
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