Chapter 21 of 27
Formula Sheet
The Dimensional Geometry — Formula Sheet
MHT-CET · Mathematics
Free The Dimensional Geometry formula sheet for MHT-CET Mathematics 2026 — all important formulas, equations, and constants for quick reference.
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Important formulas and equations from The Dimensional Geometry for MHT-CET Mathematics.
Formulas — The Dimensional Geometry
Direction Cosines and Direction Ratios
l² + m² + n² = 1Direction cosines = (±a/√(a²+b²+c²), ±b/√(a²+b²+c²), ±c/√(a²+b²+c²))Direction ratios of line joining (x₁,y₁,z₁) and (x₂,y₂,z₂) = (x₂-x₁, y₂-y₁, z₂-z₁)Equation of Line in Space
Cartesian form: (x-x₁)/a = (y-y₁)/b = (z-z₁)/cVector form: r⃗ = a⃗ + λb⃗Line through two points: (x-x₁)/(x₂-x₁) = (y-y₁)/(y₂-y₁) = (z-z₁)/(z₂-z₁)Parametric form: x = x₁ + at, y = y₁ + bt, z = z₁ + ctAngle Between Two Lines
cosθ = |a₁a₂ + b₁b₂ + c₁c₂|/√(a₁²+b₁²+c₁²)√(a₂²+b₂²+c₂²)cosθ = |l₁l₂ + m₁m₂ + n₁n₂|cosθ = |b⃗₁ · b⃗₂|/|b⃗₁||b⃗₂|Parallel condition: a₁/a₂ = b₁/b₂ = c₁/c₂Perpendicular condition: a₁a₂ + b₁b₂ + c₁c₂ = 0Shortest Distance Between Lines
d = |((b⃗₁ × b⃗₂) · (a⃗₂ - a⃗₁))|/|b⃗₁ × b⃗₂|d = |det[x₂-x₁, y₂-y₁, z₂-z₁; a₁, b₁, c₁; a₂, b₂, c₂]|/√[(b₁c₂-b₂c₁)² + (c₁a₂-c₂a₁)² + (a₁b₂-a₂b₁)²]d = |b⃗ × (a⃗₂ - a⃗₁)|/|b⃗|Distance = 0Get the complete formula sheet with derivations — continue in Super Tutor
Frequently Asked Questions
What topics are covered in The Dimensional Geometry for MHT-CET?
The Dimensional Geometry is an important chapter in MHT-CET Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Direction Cosines and Direction Ratios, Equations of Lines in Space, Angle Between Two Lines, Shortest Distance Between Two Lines.
How important is The Dimensional Geometry for MHT-CET?
The Dimensional Geometry is a frequently tested chapter in MHT-CET Mathematics. Questions from this chapter appear regularly in previous year papers. There are 390 practice questions available for this chapter.
How to prepare The Dimensional Geometry for MHT-CET?
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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