TS EAMCET · Maths · Straight Lines
Let \(A, B, C\) be three points on \(\overline{O X}, \overline{O Y}, \overline{O Z}\) respectively at the distances 3, 6, 9 from origin. Let \(Q\) be the point \((2,5,8)\) and \(P\) be the point equidistant from \(O, A, B, C\). Then, the coordinates of the point \(R\) which divides \(P Q\) in the ratio \(3: 2\) is
- A \(\left(\frac{17}{10}, \frac{29}{5}, \frac{43}{10}\right)\)
- B \(\left(\frac{7}{5}, \frac{16}{5}, 5\right)\)
- C \(\left(\frac{9}{5}, \frac{21}{5}, \frac{33}{5}\right)\)
- D \(\left(\frac{8}{5}, \frac{19}{5}, 6\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{9}{5}, \frac{21}{5}, \frac{33}{5}\right)\)
Step-by-step Solution
Detailed explanation
Let \(P\) is \((u, v, w)\). Here, \(P O^2=P A^2, P O^2=P B^2, P O^2=P C^2\) \( \begin{aligned} u^2+v^2+w^2 & =(u-3)^2+v^2+w^2 \\ u^2+v^2+w^2 & =u^2-6 u+9+v^2+u^2 \\ 6 u & =9 \Rightarrow u=\frac{3}{2} \end{aligned} \) (ii)…
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