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JEE Advanced 2024 · Paper 2 · one or more correct

JEE Advanced 2024 Mathematics question on Three Dimensional Geometry

A straight line drawn from the point P(1,3,2)P(1,3,2), parallel to the line x−21=y−42=z−61\dfrac{x-2}{1}=\dfrac{y-4}{2}=\dfrac{z-6}{1}, intersects the plane L1:x−y+3z=6L_1: x-y+3z=6 at the point Q. Another straight line which passes through Q and is perpendicular to the plane L1L_1 intersects the plane L2:2x−y+z=−4L_2: 2x-y+z=-4 at the point R. Then which of the following statements is (are) TRUE?
  1. A.
    The length of the line segment PQ is 6\sqrt{6}
  2. B.
    The coordinates of R are (1,6,3)(1,6,3)
  3. C.
    The centroid of the triangle PQR is (43,143,53)\left(\dfrac{4}{3},\dfrac{14}{3},\dfrac{5}{3}\right)
  4. D.
    The perimeter of the triangle PQR is 2+6+11\sqrt{2}+\sqrt{6}+\sqrt{11}
Show answer

Correct options: A, C

[JEE Advanced 2024 · Paper 2]

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