TS EAMCET · Maths · Three Dimensional Geometry
\(E(1,0,0), F(0,2,0), G(0,0,3)\) are respectively the mid-points of the sides \(A B, B C, C A\) of \(\triangle A B C\). If \(a_1, b_1, c_1\) and \(a_2, b_2, c_2\) are respectively the direction ratios of \(A F\) and \(B G\), then \(\frac{a_1^2+b_1^2+c_1^2}{a_2^2+b_2^2+c_2^2}=\)
- A \(\frac{26}{41}\)
- B \(\frac{13}{26}\)
- C \(\frac{17}{43}\)
- D \(\frac{13}{43}\)
Answer & Solution
Correct Answer
(A) \(\frac{26}{41}\)
Step-by-step Solution
Detailed explanation
Let the vertices of \(\triangle A B C\) are \(A\left(x_1, y_1, z_1\right), B\left(x_2, y_2, z_2\right)\) and \(C\left(x_3, y_3, z_3\right)\), so according to given informations \(\frac{x_1+x_2}{2}=1, \frac{y_1+y_2}{2}=0 \text { and } \frac{z_1+z_2}{2}=0\)…
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