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3D Geometry question

2024 · Shift 2 · Q23

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PYQ Library
JEE Advanced
Mathematics
3D Geometry
2024 · Shift 2 · Q23

3D Geometry question

2024 · Shift 2 · Q23

JEE AdvancedMathematics3D GeometryMultiple correct+4 / −2

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+3 z=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: 2 x-y+z=-4

at the point

R

. Then which of the following statements is (are) TRUE?

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

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