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MCQMediumJEE Main 2025 · 23 January, Shift 2Coordinates in 3D

Mathematics Question from JEE Main 2025 · 23 January, Shift 2

Let the point AA 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:1r : 1 (r>0r > 0). If OO is the origin and

(OQ→⋅OA→)−15∣OP→×OA→∣2=10,\left( \overrightarrow{OQ} \cdot \overrightarrow{OA} \right) - \frac{1}{5} \left|\overrightarrow{OP} \times \overrightarrow{OA}\right|^2 = 10,

then the value of rr is:

  • A

    1414

  • B

    33

  • C

    7\sqrt{7}

  • D

    77

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