Three Dimensional Geometry
CBSE · Class 12 · Mathematics
Complete topic list for Three Dimensional Geometry in CBSE Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.
Topics in Three Dimensional Geometry
Direction Cosines and Direction Ratios
- Direction cosines are cosines of angles made by a line with positive x, y, and z axes
- Direction cosines are denoted by l, m, n and satisfy l² + m² + n² = 1
- A line can be extended in two directions, giving two sets of direction cosines
Equation of a Line in Space
- A line is uniquely determined by a point and direction, or by two points
- Vector form: r⃗ = a⃗ + λb⃗ where a⃗ is position vector of point, b⃗ is direction vector
- Cartesian form: (x-x₁)/a = (y-y₁)/b = (z-z₁)/c
Angle Between Two Lines
- Angle between lines is angle between their direction vectors
- If lines don't pass through origin, draw parallel lines through origin
- Acute angle θ satisfies 0° ≤ θ ≤ 90°
Shortest Distance Between Lines
- Distance is zero if lines intersect
- For parallel lines, distance is perpendicular distance between them
- For skew lines, shortest distance is along common perpendicular
Key Concepts
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What are the important topics in Three Dimensional Geometry for CBSE Class 12 Mathematics?
Three Dimensional Geometry covers several key topics that are frequently asked in CBSE Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Three Dimensional Geometry — CBSE Class 12 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.
Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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