Chapter 20 of 42
Revision Notes
Line and Plane — Revision Notes
JEE Mains · Mathematics
Free Line and Plane revision notes for JEE Mains Mathematics 2026 — key concepts, formulas, and definitions for quick revision.
Interactive on Super Tutor
Studying Line and Plane? Get the full chapter — free.
Practice questions, revision notes, formula sheet and AI doubt-solver — built for JEE Mains Mathematics.
Super Tutor
This is just one of 27+ visuals inside Super Tutor's Line and Plane chapter
Explore the full setRevision Notes — Line and Plane
Key concepts, formulas, and definitions from Line and Plane for JEE Mains Mathematics preparation.
Key Topics to Revise
1
Direction Ratios and Direction Cosines
- Direction cosines (l, m, n) are cosines of angles a line makes with coordinate axes
- Direction ratios (a, b, c) are any three numbers proportional to direction cosines
- Key relationship: l² + m² + n² = 1
2
Equation of a Line in Space
- Vector form: r⃗ = a⃗ + λb⃗ (point a⃗, direction b⃗)
- Cartesian form: (x-x₁)/l = (y-y₁)/m = (z-z₁)/n
- Cross product form: (r⃗ - a⃗) × b⃗ = 0
3
Angle Between Lines and Distance Calculations
- Angle between lines = angle between their direction vectors
- cos θ = |b₁⃗·b₂⃗|/(|b₁⃗||b₂⃗|) for acute angle
- Lines perpendicular if b₁⃗·b₂⃗ = 0
4
Intersecting and Non-intersecting Lines
- Lines intersect if system of equations has unique solution
- Lines are parallel if direction vectors are proportional
- Lines are skew if they're neither parallel nor intersecting
Get complete revision notes with diagrams and examples — continue in Super Tutor
Key Concepts
Direction cosines (lThree main formsFor lines with direction vectors b⃗₁Distance from point P(p⃗) to lineLines can be
Frequently Asked Questions
What topics are covered in Line and Plane for JEE Mains?
Line and Plane is an important chapter in JEE Mains Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Direction Ratios and Direction Cosines, Equation of a Line in Space, Angle Between Lines and Distance Calculations, Intersecting and Non-intersecting Lines.
How important is Line and Plane for JEE Mains?
Line and Plane is a frequently tested chapter in JEE Mains Mathematics. Questions from this chapter appear regularly in previous year papers. There are 100 practice questions available for this chapter.
How to prepare Line and Plane 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.
More resources for Line and Plane
For JEE Mains aspirants
Get the full Line and Plane chapter — for free.
Practice questions, revision notes, formula sheet and AI doubt-solver for JEE Mains Mathematics.