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Jee Main 2025Medium JEE math MCQ

Let the point \( A \) divide the line segment joining the points \( P(-1,-1,2) \) and \( Q(5,5,10) \) internally in the ratio \( r : 1(r > 0) \). If \( O \) is the origin and \( \overrightarrow{OQ} \cdot \overrightarrow{OA} = \frac{1}{5} |\overrightarrow{OP} \times \overrightarrow{OA}|^2 \) = 10, then the value of \( r \) is
  1. A. \( \sqrt{7} \)
  2. B. 14
  3. C. 3
  4. D. 7

Solution

The correct option is **D**. (D. 7)

MATH

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Question
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Let the point A A divide the line segment joining the points P(1,1,2) P(-1,-1,2) and Q(5,5,10) Q(5,5,10) internally in the ratio r:1(r>0) r : 1(r > 0) . If O O is the origin and OQOA=15OP×OA2 \overrightarrow{OQ} \cdot \overrightarrow{OA} = \frac{1}{5} |\overrightarrow{OP} \times \overrightarrow{OA}|^2 = 10, then the value of r r is
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep