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Formula Sheet

Introduction To Three Dimensional Geometry — Formula Sheet

IISER Aptitude Test · Mathematics

Free Introduction To Three Dimensional Geometry formula sheet for IISER Aptitude Test Mathematics 2026 — all important formulas, equations, and constants for quick reference.

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A basic representation of the three-dimensional Cartesian coordinate system showing the X, Y, and Z axes intersecting at the origin.
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Formula Sheet — Introduction To Three Dimensional Geometry

Important formulas and equations from Introduction To Three Dimensional Geometry for IISER Aptitude Test Mathematics.

Formulas — Introduction To Three Dimensional Geometry

Coordinate System Basics

Point P = (x, y, z)

Distance Formula

PQ = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]
OP = √(x² + y² + z²)

Section Formula

Internal Division: M = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n), (mz₂+nz₁)/(m+n))
External Division: M = ((mx₂-nx₁)/(m-n), (my₂-ny₁)/(m-n), (mz₂-nz₁)/(m-n))
Midpoint: M = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2)

Centroid Formula

Centroid G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3, (z₁+z₂+z₃)/3)

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Frequently Asked Questions

What topics are covered in Introduction To Three Dimensional Geometry for IISER Aptitude Test?
Introduction To Three Dimensional Geometry is an important chapter in IISER Aptitude Test Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Coordinate System in 3D Space, Distance Formula in 3D Space, Section Formula in 3D, Centroid of Triangle.
How important is Introduction To Three Dimensional Geometry for IISER Aptitude Test?
Introduction To Three Dimensional Geometry is a frequently tested chapter in IISER Aptitude Test Mathematics. Questions from this chapter appear regularly in previous year papers. There are 110 practice questions available for this chapter.
How to prepare Introduction To Three Dimensional Geometry for IISER Aptitude Test?
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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