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3D Geometry question

2025 · Shift 1 · Q21

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PYQ Library
JEE Advanced
Mathematics
3D Geometry
2025 · Shift 1 · Q21

3D Geometry question

2025 · Shift 1 · Q21

JEE AdvancedMathematics3D GeometryMultiple correct+4 / −2

Let

L_1

be the line of intersection of the planes given by the equations

2x + 3y + z = 4

and

x + 2y + z = 5

. Let

L_2

be the line passing through the point

P(2, -1, 3)

and parallel to

L_1

. Let

M

denote the plane given by the equation

2x + y - 2z = 6

. Suppose that the line

L_2

meets the plane

M

at the point

Q

. Let

R

be the foot of the perpendicular drawn from

P

to the plane

M

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

A
The length of the line segment $PQ$ is $9\sqrt{3}$
B
The length of the line segment $QR$ is $15$
C
The area of $\triangle PQR$ is $\dfrac{3}{2}\sqrt{234}$
D
The acute angle between the line segments $PQ$ and $PR$ is $\cos^{-1}\left(\dfrac{1}{2\sqrt{3}}\right)$

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