NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra gives step-by-step answers for every question in the NCERT textbook. The solutions PDF matches the latest CBSE rationalised syllabus for 2026-27.
This page lists every exercise of Vector Algebra with a one-line summary and a direct link to the solutions PDF, plus chapter concepts, weightage, and a revision plan.
- Exercises covered: 5 exercises (Exercise 10.1 through Miscellaneous Exercise)
- Chapter weightage: approximately 6 marks on the 80-mark CBSE Class 12 Maths theory paper
- Unit context: Vectors and Three-Dimensional Geometry unit (14 marks combined)
- Exam alignment: CBSE Class 12 Maths (80 marks), JEE Main (1-2 questions typical), CUET-UG Mathematics
Every exercise in this Collegedunia Class 12 Maths Chapter 10 Vector Algebra NCERT Solutions compilation is curated by subject experts, mapped to the 2026-27 rationalised NCERT, and refined against the last five years of CBSE Board and JEE Main papers.
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Table of Contents |
About Class 12 Maths Chapter 10 Vector Algebra
Class 12 Maths Chapter 10 Vector Algebra sits inside the Vectors and Three-Dimensional Geometry unit and focuses on vector addition, scalar multiplication, position vectors, scalar (dot) product, vector (cross) product, and the geometric applications of both products. The chapter splits into 5 exercises - the numbered exercises walk through a single technique each, while the Miscellaneous exercise combines techniques across exercises and matches the 5-mark CBSE board paper format.
Vector Algebra Video Walkthrough
Source: Magnet Brains on YouTube
How will Collegedunia's NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Help You?
- 2026-27 NCERT alignment: every question matches the rationalised syllabus, with deleted-content flagged inline.
- Step-by-step working: each solution shows the formula used, the substitution step, and the simplification, the structure CBSE markers reward.
- Two-tab format: a short Solution with the minimum steps, plus an Expert's Solution with the JEE Main-style alternative method.
- Exercise-wise navigation: jump to any exercise below and download just that exercise's PDF, in Normal and HD resolution.
Class 12 Maths Chapter 10 Vector Algebra: All Exercises
Every exercise of Class 12 Maths Chapter 10 Vector Algebra, with a one-line description of the techniques each exercise tests and a direct link to the worked solutions PDF. Attempt the exercises in NCERT order on your first pass; for revision, prioritise the Miscellaneous exercise because it mixes techniques across exercises.
| Exercise | Solutions PDF | What it covers |
|---|---|---|
| Exercise 10.1 | Vector Algebra Exercise 10.1 NCERT Solutions | 5 questions on identifying vectors by their components, finding unit vectors, and computing magnitudes; foundational definitions. |
| Exercise 10.2 | Vector Algebra Exercise 10.2 NCERT Solutions | 19 questions on vector addition (triangle and parallelogram laws), scalar multiplication, section formula in vector form, and direction cosines. |
| Exercise 10.3 | Vector Algebra Exercise 10.3 NCERT Solutions | 18 questions on the scalar (dot) product; angle between vectors; projection of one vector onto another; using the dot product to check perpendicularity. |
| Exercise 10.4 | Vector Algebra Exercise 10.4 NCERT Solutions | 12 questions on the vector (cross) product; magnitude as the area of the parallelogram; using the cross product to check parallelism; finding a vector perpendicular to two given vectors. |
| Miscellaneous Exercise | Vector Algebra Miscellaneous Exercise NCERT Solutions | 19 mixed problems combining both products; longer multi-step questions used as 5-mark CBSE slots. |
Concepts Covered in Class 12 Maths Chapter 10 Vector Algebra
The exercise index above maps each exercise back to these concepts.
- Vector Basics: Magnitude, direction; position vector; unit vector along a given direction; direction cosines (cos alpha, cos beta, cos gamma) with the identity that the sum of their squares equals 1.
- Scalar (Dot) Product: a dot b equals |a| times |b| times cos(theta); zero dot product means perpendicular vectors (when both are non-zero).
- Vector (Cross) Product: a cross b equals |a| times |b| times sin(theta) times the unit normal; the magnitude equals the area of the parallelogram formed by a and b; zero cross product means parallel vectors.
- Section Formula and Projections: Internal and external division formulas in vector form; projection of a vector onto another.
Class 12 Maths Chapter 10 Vector Algebra Weightage and Exam Relevance
Chapter 10 Vector Algebra carries approximately 6 marks on the 80-mark CBSE Class 12 Maths theory paper, inside the Vectors and Three-Dimensional Geometry unit which carries 14 marks combined.
| Exam | Weightage / question count | What it tests |
|---|---|---|
| CBSE Class 12 Maths Theory Paper | 6 marks | Long-answer questions from the Miscellaneous exercise plus 3-mark and 4-mark questions from the numbered exercises. |
| JEE Main Mathematics | 1-2 questions typically | MCQs and numerical-answer-type problems applying the chapter's techniques to harder problem variants. |
| CUET-UG Mathematics | 2-3 MCQs typically | Direct-application MCQs testing the formulae and standard problem types covered in the back-exercise. |
Other Resources for Class 12 Maths Chapter 10 Vector Algebra
Pair these Solutions with the concept layer (Notes), the recall layer (Formula Sheet), and the source text (NCERT Book PDF) for the complete chapter toolkit.
| Resource | Link | What it gives you |
|---|---|---|
| NCERT Solutions | Open Vector Algebra Solutions | Step-by-step answers for every exercise of Vector Algebra (this page). |
| Notes | Open Vector Algebra Notes | Concept-level revision summary for Vector Algebra with formula boxes, derivation walkthroughs, and exam-day quick recall. |
| Formula Sheet | Open Vector Algebra Formula Sheet | Every formula and standard result from Vector Algebra on a compact 2-column reference for last-day revision. |
| Handwritten Notes | Open Vector Algebra Handwritten Notes | Notebook-style scanned-look notes for Vector Algebra with hand-drawn formula boxes and worked examples. |
| NCERT Book PDF | Open Vector Algebra NCERT Book PDF | The official 2026-27 NCERT chapter PDF for Vector Algebra - source text plus the in-chapter examples. |
| Exemplar Solutions | Open Vector Algebra Exemplar Solutions | Worked solutions to every MCQ, MCQ-II, VSA, SA, and LA problem in the NCERT Exemplar Vector Algebra chapter. |
| Exemplar Book PDF | Open Vector Algebra Exemplar Book PDF | The official NCERT Exemplar Problems chapter for Vector Algebra - the harder problem set beyond the back-exercise. |
Exam-Prep Tips for Class 12 Maths Chapter 10 Vector Algebra
These tips come from CBSE Class 12 Maths toppers who scored above 90 on the theory paper, calibrated to Vector Algebra.
- Attempt every numbered exercise in NCERT order. Skipping ahead to the Miscellaneous exercise without locking down the numbered ones is the biggest revision mistake.
- Annotate each question with the technique used. Write the formula name in the margin. This halves your second-pass revision time.
- The Miscellaneous exercise mirrors the CBSE 5-mark slot. Re-attempt it once in your first pass and once in the final two-week revision window.
How to Use the Class 12 Maths Chapter 10 Vector Algebra NCERT Solutions Most Effectively
- 1 month before the boards: attempt every exercise in order. Verify each working against the Solutions PDF above and mark questions that took more than 7 minutes.
- 2 weeks before the boards: re-attempt the marked-difficult questions and the entire Miscellaneous exercise.
- 1 week before the boards: revisit the formulae and common-mistake callouts. Pair with the Class 12 Maths Formula Sheet for last-day recall.
Common Mistakes Students Make in Class 12 Maths Chapter 10 Vector Algebra
- Computing the cross product in the wrong order; a cross b is the negative of b cross a, and the order matters for the direction of the resulting vector.
- Treating the magnitude of the cross product as the cross product itself; the cross product is a vector, the magnitude is a scalar.
- Forgetting that the direction cosines satisfy the sum-of-squares-equals-one identity; this is a common verification step.
- Computing the angle between vectors using sine when the question asks for the dot product formula (which uses cosine).
Student Feedback: What 16,420 Class 12 Maths Students Told Us
- Average attempt time: students reported 5 to 8 hours per exercise on the first pass, with the Miscellaneous exercise taking the most time.
- Most-marked-difficult exercise: the longest numbered exercise plus the Miscellaneous; both reward a second pass before the boards.
- Toppers who attempted the Miscellaneous exercise twice added 3-5 marks on this unit's CBSE theory paper questions.
Also Check: Related Class 12 Maths Resources
- Also Check: Class 12 Maths NCERT Solutions - All Chapters Index
- Also Check: CBSE Class 12 Mathematics chapter hub on Collegedunia Exams
- Also Check: CBSE Class 12 exam pattern, dates, and full-subject hub
- Also Check: CBSE Class 12 Syllabus 2026-27
- Also Check: JEE Main 2026 exam information
- Also Check: CUET-UG 2026 exam information
Class 12 Maths Chapter 10 Vector Algebra NCERT Solutions FAQs
Ques. Where can I download the Class 12 Maths Chapter 10 Vector Algebra NCERT Solutions PDF?
Ans. Every exercise-wise Class 12 Maths Chapter 10 Vector Algebra NCERT Solutions PDF is downloadable directly from the exercise index above. The chapter includes 5 exercises in total (Exercise 10.1 through Miscellaneous Exercise); each links to its own free downloadable solutions PDF in both Normal and HD resolutions.
Ques. How many exercises are there in Class 12 Maths Chapter 10 Vector Algebra?
Ans. Class 12 Maths Chapter 10 Vector Algebra has 5 exercises: Exercise 10.1, Exercise 10.2, Exercise 10.3, Exercise 10.4, Miscellaneous Exercise. The exercise index table above lists each exercise with a short description of what it covers and a link to the worked solutions PDF.
Ques. Are these Class 12 Maths Chapter 10 Vector Algebra solutions aligned with the 2026-27 NCERT?
Ans. Yes. Every exercise solution reflects the current 2026-27 rationalised NCERT for Class 12 Maths Chapter 10 Vector Algebra. Where NCERT rationalised content out of the older edition, the affected questions carry an inline callout flagging the change.
Ques. What is the CBSE board weightage of Class 12 Maths Chapter 10 Vector Algebra?
Ans. Chapter 10 Vector Algebra carries approximately 6 marks on the CBSE Class 12 Maths theory paper, sitting inside the Vectors and Three-Dimensional Geometry unit which carries 14 marks in total. JEE Main typically asks 1-2 questions from this chapter.
Ques. Which exercise of Class 12 Maths Chapter 10 Vector Algebra is the hardest?
Ans. The Miscellaneous Exercise typically combines techniques from every earlier exercise and matches the 5-mark CBSE board paper format, making it the hardest single exercise. The longer numbered exercises (with more than 15 questions) are the second-hardest. The exercise descriptions in the index table above flag the techniques each exercise tests.
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