JEE Advanced Three Dimensional Geometry — previous year questions

37 questions from 2026, 2025, 2024, 2023, 2022, 2020, 2019, 2018, 2016, 2015, 2014, 2013, 2012, 2010, 2009, 2008, 2007.

Let P be the plane such that it contains the straight line (x-1)/2 = (y-3)/3 = (z+2)/1 and is perpendicular…2026JEE Advanced
Let L₁ be the line of intersection of the planes given by the equations 2x + 3y + z = 4 and x + 2y + z = 5.…2025JEE Advanced
Let L be the straight line joining the points P(1, 2, -1) and Q(2, 3, 1). Let S be the foot of the…2024JEE Advanced
and L₂: /3 = /2 = /γ intersect. Let R₁ be the point of intersection of L₁ and L₂. Let O = (0, 0, 0), and n̂…2024JEE Advanced
Let OP = ((α−1)/α) î + ĵ + k̂, OQ = î + ((β−1)/β) ĵ + k̂ and OR = î + ĵ + (1/2) k̂ be three vectors, where a,…2024JEE Advanced
Let R denote the three-dimensional space. Take two points P=(1,2,3) and Q=(4,2,7). Let dist(X, Y) denote the…2024JEE Advanced
A straight line drawn from the point P(1, 3, 2), parallel to the line (x-2)/1 = (y-4)/2 = (z-6)/1, intersects…2024JEE Advanced
Let Q be the cube with the set of vertices {(x₁, x₂, x₃) ∈ R³ : x₁, x₂, x₃ ∈ {0,1}}. Let F be the set of all…2023JEE Advanced
Let P be the plane √3x + 2y + 3z = 16 and let S = {αî + βĵ + γk̂ : α² + β² + γ² = 1 and the distance of (α,…2023JEE Advanced
Let ell₁ and ell₂ be the lines r⃗₁ = λ(î + ĵ + k̂) and r⃗₂ = (ĵ - k̂) + μ(î + k̂), respectively. Let X be…2023JEE Advanced
Let P₁ and P₂ be two planes given by P₁: 10x + 15y + 12z - 60 = 0, P₂: -2x + 5y + 4z - 20 = 0. Which of the…2022JEE Advanced
Let S be the reflection of a point Q with respect to the plane given by r⃗=-(t+p)î+tĵ+(1+p)k̂ where t,p are…2022JEE Advanced
Let L₁ and L₂ be the following straight line. L₁: (x-1)/1 = y/(-1) = (z-1)/3 and L₂: (x-1)/(-3) = y/(-1) =…2020JEE Advanced
Let α, β, γ, δ be real numbers such that α² + β² + γ² ≠ 0 and α + γ = 1. Suppose the point (3, 2, -1) is the…2020JEE Advanced
Three lines L₁ : r⃗ = λî, λ ∈ R, L₂ : r⃗ = k̂ + μĵ, μ ∈ R and L₃ : r⃗ = î + ĵ + νk̂, ν ∈ R are given. For…2019JEE Advanced
Let L₁ and L₂ denote the lines r⃗ = î + λ(-î + 2ĵ + 2k̂), λ ∈ R and r⃗ = μ(2î - ĵ + 2k̂), μ ∈ R…2019JEE Advanced
Three lines are given by r⃗ = λ î, λ ∈ R; r⃗ = μ(î + ĵ), μ ∈ R and r⃗ = v(î + ĵ + k̂), v ∈ R. Let the…2019JEE Advanced
Let P be a point in the first octant, whose image Q in the plane x + y = 3 (that is, the line segment PQ is…2018JEE Advanced
Let P₁ : 2x + y - z = 3 and P₂ : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is…2018JEE Advanced
Consider a pyramid OPQRS located in the first octant (x ≥ 0, y ≥ 0, z ≥ 0) with O as origin, and OP and OR…2016JEE Advanced
In R³, let L be a straight line passing through the origin. Suppose that all the points on L are at a…2015JEE Advanced
In R³, consider the planes P₁ : y = 0 and P₂ : x + z = 1. Let P₃ be the plane, different from P₁ and P₂,…2015JEE Advanced
From a point P(λ, λ, λ), perpendicular PQ and PR are drawn respectively on the lines y = x, z = 1 and y = -x,…2014JEE Advanced
A line l passing through the origin is perpendicular to the lines l₁ : (3+t)î + (-1+2t)ĵ + (4+2t)k̂, -∞ < t…2013JEE Advanced
Two lines L₁ : x=5, y/(3-α)=z/(-2) and L₂ : x=α, y/(-1)=z/(2-α) are coplanar. Then α can take value(s)2013JEE Advanced
Consider the lines L₁ : (x-1)/2 = y/(-1) = (z+3)/1, L₂ : (x-4)/1 = (y+3)/1 = (z+3)/2 and the planes P₁ : 7x +…2013JEE Advanced
The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x - y + z…2012JEE Advanced
The point P is the intersection of the straight line joining the points Q(2, 3, 5) and R(1, -1, 4) with the…2012JEE Advanced
If the straight lines (x-1)/2=(y+1)/k=z/2 and (x+1)/5=(y+1)/2=z/k are coplanar, then the plane (s) containing…2012JEE Advanced
If the distance of the point P(1,-2,1) from the plane x+2y-2z=α, where α>0, is 5, then the foot of the…2010JEE Advanced
Equation of the plane containing the straight line x/2 = y/3 = z/4 and perpendicular to the plane containing…2010JEE Advanced
If the distance between the plane x-2y+z=d and the plane containing the lines (x-1)/2=(y-2)/3=(z-3)/4 and…2010JEE Advanced
A line with positive direction cosines passes through the point P(2,-1,2) and makes equal angles with the…2009JEE Advanced
Let P(3, 2, 6) be a point in space and Q be a point on the line r⃗ = (î - ĵ + 2k̂) + μ(-3î + ĵ + 5k̂).…2009JEE Advanced
Consider three planes P₁ : x-y+z=1; P₂ : x+y-z=-1; P₃ : x-3y+3z=2 Let L₁, L₂, L₃ be the lines of intersection…2008JEE Advanced
A line AB in three-dimensional space makes angles 45^∘ and 120^∘ with the positive x-axis and the positive…2007JEE Advanced
Consider the planes 3x - 6y - 2z = 15 and 2x + y - 2z = 5. Statement - I : The parametric equations of the…2007JEE Advanced

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