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Mathematics: Calculus
Class 12PDF
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Mathematics · Class 12Three Dimensional GeometryVideo coming soonRead the notes instead
Free notes for this chapterMark as Completed
Direction Cosines and Ratios, Equation of a Line, Angle between Two Lines and the board questions built on them — roughly 5 marks of the paper.
What this chapter covers
- 1Direction Cosines and Ratios
- 2Equation of a Line
- 3Angle between Two Lines
- 4Shortest Distance
These lessons are being recorded. The written notes for this chapter are free to download now.
Learning resources
Seedha Notes
Chapter notes withimportant points,examples & format
View Notes for Three Dimensional Geometry, MathematicsPractice Questions
Important questions,board questions,numericals
Practice Now for Three Dimensional Geometry, MathematicsPrevious yearquestions withfull solutions
View PYQs for Three Dimensional Geometry, MathematicsSample Paper
Board patternsample paper withmarking scheme
Open Paper for Three Dimensional Geometry, Mathematics
In the notes
Topics covered
- 01Direction Cosines and Ratios20:14
- 02Equation of a Line19:50
- 03Angle between Two Lines30:05
- 04Shortest Distance20:41
After this chapter you can
- Explain direction cosines and ratios without reading from the book
- Present equation of a line in the format the marking scheme rewards
- Attempt every previous year question set on this chapter
- Marks
- 5
- PYQs
- 11
- Video
- 1h 31m
Then do the work
- One-shot revision, 23 minutes
- Formula sheet for this chapter
- Printable summary, 2 pages
Prepare
| Year | Asked as | Marks |
|---|---|---|
| 2025 | Long answer | 2 |
| 2024 | Short answer | 6 |
| 2023 | Case based | 2 |
| 2022 | MCQ set | 6 |
| 2021 | Long answer | 4 |
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