Straight Lines · JEE Advanced previous year questions

2024 1 question

1. Q62024 · 26 May 2024 · Paper 2· One or more correct

   A straight line drawn from the point $P(1,3,2)$, parallel to the line $\frac{x-2}{1}=\frac{y-4}{2}=\frac{z-6}{1}$, intersects the plane $L_1:x-y+3z=6$ at the point $Q$. Another straight line which passes through $Q$ and is perpendicular to the plane $L_1$ intersects the plane $L_2:2x-y+z=-4$ at the point $R$. Then which of the following statements is (are) TRUE?

   1. A.The length of the line segment $PQ$ is $\sqrt{6}$
   2. B.The coordinates of $R$ are $(1,6,3)$
   3. C.The centroid of the triangle $PQR$ is $\left(\frac{4}{3},\frac{14}{3},\frac{5}{3}\right)$
   4. D.The perimeter of the triangle $PQR$ is $\sqrt{2}+\sqrt{6}+\sqrt{11}$
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   Answer: A, C