JEE Advanced Introduction to 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 to…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
Let γ ∈ R be such that the lines L₁: (x+11)/1 = (y+21)/2 = (z+29)/3 and L₂: (x+16)/3 = (y+11)/2 = (z+4)/γ…2024JEE Advanced
Let OP⃗ = (α - 1)/αî + ĵ + k̂, OQ⃗ = î + (β - 1)/βĵ + k̂ and O̅R̅ = î + ĵ + 1/2k̂ be three vectors,…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)…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 the set…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 following…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…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 : r = λî, λ ∈ R, L₂ : r = 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 = λî, λ ∈ R ; r⃗ = μ(î + ĵ), μ ∈ R and r⃗ = ν(î + ĵ + k̂), ν ∈ 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, which…2015JEE Advanced
From a point P(λ, λ, λ), perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y =…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)…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…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 Ax - 2y + z = d and the plane containing the lines (x-1)/2 = (y-2)/3 =…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…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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