Chapter 21 of 27
Formula Sheet
The Dimensional Geometry — Formula Sheet
CG PET · Mathematics
All important formulas from The Dimensional Geometry for CG PET Mathematics. Quick reference for revision and problem solving.
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Important formulas and equations from The Dimensional Geometry for CG PET 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 CG PET?
The Dimensional Geometry is an important chapter in CG PET 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 CG PET?
The Dimensional Geometry is a frequently tested chapter in CG PET Mathematics. Questions from this chapter appear regularly in previous year papers. There are 316 practice questions available for this chapter.
How to prepare The Dimensional Geometry for CG PET?
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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