JEE Advanced Three Dimensional Geometry questions with solutions
Lines and planes in space. 23 questions from our 2016–2025 JEE Advanced pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.
Also practise: Three Dimensional Geometry for JEE Main
JEE Advanced 2025
JEE Advanced 2024
JEE Advanced 2022
- A plane contains the line (x-1)/(2)=(y+1)/(1)=(z-2)/(-1) and the point (1,2,3). Find the volume of the tetrahedron bounded by this plane and the…
- Vec r=(1,2,3)+λ(1,1,1) and L2: vec r=(0,1,-1)+μ(2,1,0). If d denotes the shortest distance between L1 and L2, then 2d^2 equals
- A plane contains the line L: (x-1)/(2)=(y)/(-1)=(z-2)/(2) and also passes through the point P(3,4,1). The perpendicular distance of the origin from…
JEE Advanced 2021
JEE Advanced 2020
- Let L1:(x-1)/(1)=(y-2)/(-1)=(z-3)/(2) and L2:(x-2)/(2)=(y-1)/(1)=(z)/(-1). Let Pi be the plane containing L1 and parallel to L2. The perpendicular…
- Line L1 is given by the planes 2x-y=0 and y-z=0. Line L2 is given by the planes x-2y=3 and 2y+z=0. Let d be the shortest distance between L1 and L2.…
- Let S be the sphere x^2+y^2+z^2-2x-4y-6z+10=0 and let Pi be the plane x+y+z=3. The plane Pi cuts S in a circle C.
JEE Advanced 2019
JEE Advanced 2018
- Let L1: (x-1)/(1)=(y-2)/(2)=(z-3)/(2) and L2: (x-3)/(2)=(y-1)/(1)=(z)/(-2).
- The sphere S: x^2+y^2+z^2-2x+4y-6z-2=0 is cut by the plane Pi: 2x-y+2z=1 in a circle Gamma.
- A variable plane is at a constant distance 2 from the origin and meets the coordinate axes at A, B, C. The centroid of triangle ABC lies on the…
JEE Advanced 2017
- (x-1)/(1)=(y-2)/(-1)=(z-3)/(2) and L2: (x-4)/(2)=y/1=(z+1)/(-1).
- The line L: (x-1)/(2)=y/1=(z+1)/(-1) and the point P(0,1,2) are given. The perpendicular distance of the origin from the plane that contains L and…
- Vec r=λ(hat i+2hat j+2hat k) and L2: vec r=(3hat i+3hat k)+μ(2hat i+hat j-2hat k), where λ,μ∈mathbb R.
JEE Advanced 2016
Other Mathematics topics
Area Under Curves 13Binomial Theorem 10Complex Numbers 24Conic Sections 34Differential Equations 18Differentiation and Application of Derivatives 20Indefinite and Definite Integrals 18Limits 19Matrices and Determinants 28Permutations and Combinations 18Probability 38Quadratic Equations 12Sequences and Series 11Sets, Relations and Functions 8Straight Lines and Circles 10Trigonometry and Inverse Trigonometric Functions 18Vector Algebra 9