3D Geometry is part of the JEE Advanced Mathematics syllabus and carries 8% weightage in the JEE Advanced Question Paper, generally 3-4 questions are asked from this topic.
3D Geometry is the mathematics of shapes in three dimensional spaces which comprises three coordinates i.e. x coordinate, y coordinate and z coordinate. 3D Geometry is considered to be of moderately tough with major focus on subtopics such as Distance Between Planes, Angle Between Lines & Planes.
Must Read Articles:
- Download JEE Advanced Syllabus 2025
- Download JEE Advanced 2024 Paper With Detailed Solutions
- JEE Advanced Previous Year Question Paper PDF Download
The 3D Geometry questions with detailed solutions asked in JEE Main are listed below:
Question 1:
Let R3 denote the three-dimensional space. Take two points P = (1, 2, 3) and Q = (4, 2 ,7). Let dist(X, Y) denote the distance between two points X and Y in R3.
Let S={X∈R3:(dist(X,P)2)−(dist(X,Q))2=50} and
T={Y∈R3:(dist(Y,Q))2−(dist(Y,P))2=50}
Then which of the following statements is (are) TRUE ?
- There is a triangle whose area is 1 and all of whose vertices are from S.
- There are two distinct points L and M in T such that each point on the line segment LM is also in T.
- There are infinitely many rectangles of perimeter 48, two of whose vertices are from S and the other two vertices are from T.
- There is a square of perimeter 48, two of whose vertices are from S and the other two vertices are from T.
Question 2:
A straight line drawn from the point P(1,3, 2), parallel to the line
x−21=y−42=z−61, intersects the plane L1 : x - y + 3z = 6 at the point Q. Another straight line which passes through Q and is perpendicular to the plane L1 intersects the plane L2 : 2x - y + z = -4 at the point R. Then which of the following statements is (are) TRUE ?
Question 3:
Question 4:
Let S be the reflection of a point Q with respect to the plane given by
r=−(t+p)i^+tj^+(1+p)k^ where t,p are real parameters and
i^,j^,k^ are the unit vectors along the three positive coordinate axes. If the position vectors of Q and S are 10i^+15j^+20k^
and αi^+βj^+γk^ respectively, then which of the following is/are TRUE ?
- 3(α+β)=−101
- 3(β+γ)=−71
- 3(γ+α)=−86
- 3(α+β+γ)=−121
Question 5:
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 straight lines can be an edge of some tetrahedron whose two faces lie on
P1 and P2 ?
Question 6:
Consider the lines L1 and L2 defined by L1:x2+y−1=0 and
L2:x2−y+1=0 . For a fixed constant λ, let C be the locus of a point P such that the product of the distance of P from L1 and the distance of P from L2 is λ2. The line
y=2x+1 meets C at two points R and S, where the distance between R and S is
270.
Let the perpendicular bisector of RS meet C at two distinct points R’ and S’. Let D be the square of the distance between R’ and S’.
The value of λ2 is _______ ?
Question 7:
In a triangle PQR, let a=QR→,b=RP→ and
c=PQ→ If
Question 8:
The equation of the plane passing through the point (1,1,1) and perpendicular to the planes $2
- $14
- $14
- $14
- $-14
JEE Advanced Exam Pattern 2025
- Mode of the exam: The examination was conducted ONLY in the Computer Based Test (CBT) mode.
- Number of papers: Two question papers: Paper 1 and Paper 2 of three hours duration each. Both papers are compulsory.
- Language: English and Hindi
- Total duration: 6 hours
- Number of sections: Each question paper consisted of three separate sections, viz., Physics, Chemistry and Mathematics.
- Marking scheme: Details of the marking scheme were provided in the “Instructions to Candidates” section at the time of examination. The same is also explained further below.
JEE Advanced 2025 Mathematics Syllabus
JEE Advanced Mathematics Syllabus consists of nine units- Sets, Relations and Functions ; Algebra ; Matrices; Probability and Statistics; Trignometry; Analytical Geometry; Differential Calculus ; Integral Calculus and Vectors. Check JEE Advanced 2025 Syllabus
JEE Advanced Mathematics Syllabus according to the seven units is defined below.
| Units | Sub Units |
|---|---|
| Sets, Relations, and Functions | - Sets and their representations, different kinds of sets (empty, finite, and infinite), algebra of sets, intersection, complement, difference, and symmetric difference of sets and their algebraic properties, De-Morgan’s laws on union, intersection, and difference (for finite number of sets), and practical problems based on them.- Cartesian product of finite sets, ordered pair, relations, domain, and codomain of relations, equivalence relation.- Function as a special case of relation, functions as mappings, domain, codomain, range of functions, invertible functions, even and odd functions, into, onto and one-to-one functions, special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer, etc.), sum, difference, product, and composition of functions. |
| Algebra | - Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.- Statement of fundamental theorem of algebra, quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.- Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite arithmetic and geometric progressions, infinite geometric series, sum of the first n natural numbers, sums of squares and cubes of the first n natural numbers.- Logarithms and their properties, permutations and combinations, binomial theorem for a positive integral index, properties of binomial coefficients. |
| Matrices | - Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, elementary row and column transformations, determinant of a square matrix of order up to three, adjoint of a matrix, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric, and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables. |
| Probability and Statistics | - Random experiment, sample space, different types of events (impossible, simple, compound), addition and multiplication rules of probability, conditional probability, independence of events, total probability, Bayes Theorem, computation of probability of events using permutations and combinations.- Measure of central tendency and dispersion, mean, median, mode, mean deviation, standard deviation, and variance of grouped and ungrouped data, analysis of the frequency distribution with the same mean but different variance, random variable, mean, and variance of the random variable. |
| Trigonometry | - Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.- Inverse trigonometric functions (principal value only) and their elementary properties. |
| Analytical Geometry | - Topics related to coordinate geometry, straight lines, circles, conic sections, and other geometric properties. |
| Differential Calculus | - Concepts of limits, continuity, differentiation, derivatives of functions, application of derivatives, increasing and decreasing functions, maxima and minima. |
| Integral Calculus | - Indefinite and definite integrals, properties of integrals, fundamental theorem of calculus, methods of integration, applications of integration. |
| Vectors | - Vectors and their properties, operations on vectors, scalar and vector products, applications in geometry and physics. |
However, based on the previous year's analysis, the chapters along with the number of questions and marks tabulated below:
| Chapter Name | Number of Questions | Marks |
|---|---|---|
| Application of Derivatives | 3 | 9 |
| Ellipse | 1 | 3 |
| Circles | 2 | 6 |
| Parabola | 2 | 7 |
| Definite Integral | 2 | 7 |
| Permutations and Combinations | 1 | 3 |
| Sequence and Series | 1 | 3 |
| Matrices | 2 | 7 |
| Limit and Continuity | 1 | 4 |
| Probability | 1 | 4 |
| Complex Numbers | 1 | 4 |
| Hyperbola | 1 | 4 |
JEE Advanced - Marks wise Weightage of Topics
| Topics | Marks |
|---|---|
| Calculus | 40-50 marks |
| Vector and 3D Geometry | 15-20 marks |
| Probability & Permutation & Combination | 15-20 marks |
| Parabola, Hyperbola, Ellipse, Rectangular Hyperbola | 15 marks |
| Complex Numbers | 15 marks |
Important Books for Mathematics:
JEE Advanced 2024 Question Paper PDF with Solutions
| Paper Name | Question Paper Link | Solutions Link |
|---|---|---|
| JEE Advanced 2024 Paper 1 Question Paper (English) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 2 Question Paper (English) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 1 Question Paper (Hindi) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 1 Question Paper (Hindi) | Download PDF | Check Solutions |
JEE Advanced Last 5 Year Mathematics Papers Pdf
Download free JEE Advanced Previous Year Question Paper PDFs from the table provided below:-
| JEE Advanced Paper Name | Question Paper Link |
|---|---|
| JEE Advanced 2024 Question Paper PDF | Click Here |
| JEE Advanced 2023 Question Paper PDF | Click Here |
| JEE Advanced 2022 Question Paper PDF | Click Here |
| JEE Advanced 2021 Question Paper PDF | Click Here |
| JEE Advanced 2020 Question Paper PDF | Click Here |
| JEE Advanced 2019 Question Paper PDF | Click Here |
| JEE Advanced 2018 Question Paper PDF | Click Here |
| JEE Advanced 2017 Question Paper PDF | Click Here |
| JEE Advanced 2016 Question Paper PDF | Click Here |
JEE Advanced 2023 Question Paper PDF Download With Solutions
| Paper | Question Paper PDF | Answer Key PDF |
|---|---|---|
| Question Paper 1 PDF | Download PDF | Check Solutions |
| Question Paper 2 PDF | Download PDF | Check Solutions |
| Question Paper AAT PDF | Download PDF | Check Solutions |
JEE Advanced 2022 Question Paper
| 2022 Question Paper | PDF Download |
|---|---|
| Question Paper 1 PDF | Click here |
| Question Paper 2 PDF | Click here |
JEE Advanced 2021 Question Paper
| Question Paper | PDF Download | ||
|---|---|---|---|
| Question Paper 1 PDF | Physics | Chemistry | Maths |
| Question Paper 2 PDF | Physics | Chemistry | Maths |
JEE Advanced 2020 Question Paper
| Question Paper | PDF Download |
| Question Paper 1 PDF | Click here |
| Question Paper 2 PDF | Click here |
Frequently Asked Questions
What is the concept of 3D Geometry?
3D Geometry refers to the mathematics of shapes in three-dimensional spaces. These shapes comprise three coordinates: x-coordinate, y-coordinate and z-coordinate. In three-dimensional spaces there is a requirement of three parameters to find the exact location of a point.
Is 3D Geometry easy in Class 12th?
Class 12th 3D Geometry is considered to be moderately tough and one of the most scoring chapters in mathematics. 3D geometry focuses on lines, planes, angles and three dimensional spaces. The candidate should be thorough with the related formulas to solve the numerical questions and maximize their overall score.
What does 3D mean in Geometry?
In geometry, three dimensional shapes refer to solids that have three dimensions such as length, width and height which is different from two dimensional shapes as they only have two dimensions, length and width. Some examples of three dimensional shapes are: cubical box, ball or a conical hat.
Is 3D Geometry important for JEE Advanced exam 2025?
Yes, 3D Geometry is important for JEE Advanced exam for understanding the direction of lines and vectors in 3D spaces. Keeping these concepts clear is important for solving different numerical problems related to lines and planes. Understanding the concepts of this chapter is especially important for candidates aiming for the B.Arch courses in the top IITs.
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