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Introduction to 3D Geometry — Syllabus

JEE Mains · Mathematics

Free Introduction to 3D Geometry syllabus for JEE Mains Mathematics 2026 — topics covered, weightage, and preparation priorities for this chapter.

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An illustration of a three-dimensional Cartesian coordinate system with X, Y, and Z axes, showing a point P(x, y, z) and its projections onto the coordinate planes to help visualize 3D space.
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Introduction to 3D Geometry — Syllabus & Topics

Topics covered in Introduction to 3D Geometry for JEE Mains Mathematics.

Topics in Introduction to 3D Geometry

1

3D Coordinate System and Point Location

  • Three mutually perpendicular axes (x, y, z) divide 3D space into 8 octants
  • Any point P(x, y, z) has signed distances from coordinate planes: |x| from yz-plane, |y| from xz-plane, |z| from xy-plane
  • Coordinate planes have equations: xy-plane (z=0), yz-plane (x=0), xz-plane (y=0)
2

Distance Formula in 3D

  • Extension of 2D distance formula to include z-coordinate difference
  • Projections of line segments on coordinate axes give component distances
  • Distance formula applies to prove collinearity, right triangles, and geometric properties
3

Section Formula in 3D

  • Internal division: Point divides line segment from inside, ratio m:n gives positive values
  • External division: Point divides line segment from outside, ratio m:n with one negative component
  • Midpoint formula is special case of internal division with ratio 1:1
4

Spheres in 3D Geometry

  • Sphere is locus of points equidistant from a fixed center point
  • Standard form uses center-radius relationship directly
  • General form can be converted to standard form by completing squares

Key Concepts

Three mutually perpendicular axes (xDistance between two points P(x₁For internal division in ratio mStandard formLine parallel to x

Frequently Asked Questions

What topics are covered in Introduction to 3D Geometry for JEE Mains?
Introduction to 3D Geometry is an important chapter in JEE Mains Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: 3D Coordinate System and Point Location, Distance Formula in 3D, Section Formula in 3D, Spheres in 3D Geometry.
How important is Introduction to 3D Geometry for JEE Mains?
Introduction to 3D Geometry is a frequently tested chapter in JEE Mains Mathematics. Questions from this chapter appear regularly in previous year papers. There are 52 practice questions available for this chapter.
How to prepare Introduction to 3D Geometry for JEE Mains?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.

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