Class 12 Mathematics — Chapter 10: Vector Algebra
66 practice questions · 22 Easy · 22 Medium · 22 Hard
Practise Class 12 Mathematics Chapter 10, "Vector Algebra", with 66 NCERT-aligned multiple-choice questions. The set is split into 22 Easy, 22 Medium and 22 Hard questions, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams, JEE Main and JEE Advanced.
"Vector Algebra" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+2 correct, −1 wrong, 0 skipped), training the same accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Vector Algebra, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 12 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 66.
Key concepts: Vector Algebra (Class 12 Mathematics)
This chapter introduces vectors, their types and operations, and the dot and cross products with their geometric meaning.
- Vectors and types
- A vector has magnitude and direction; types include zero, unit, equal, collinear and position vectors.
- Components & magnitude
- For a = xî + yĵ + zk̂, the magnitude is |a| = √(x² + y² + z²); a unit vector is a/|a|.
- Dot (scalar) product
- a·b = |a||b|cosθ — a scalar; it is zero for perpendicular vectors and gives projections.
- Cross (vector) product
- a×b = |a||b|sinθ n̂ — a vector perpendicular to both; its magnitude is the area of the parallelogram on a and b.
- Section formula
- The position vector of a point dividing a line in a given ratio is found by the section formula.
Key formulas — Vector Algebra
💡 Exam tips for Vector Algebra
- Use the dot product to test perpendicularity (a·b = 0) and the cross product for parallelism (a×b = 0).
- Area of a triangle on vectors a and b is ½|a×b|.
Sample questions
Magnitude of (3,4):
√(9+16) = 5.
a · b = |a||b| ___
Standard dot product.
|a × b| equals area of:
Triangle area = ½|a × b|.
Vector Algebra — FAQs
What are the key concepts in Class 12 Mathematics Vector Algebra?+
This chapter introduces vectors, their types and operations, and the dot and cross products with their geometric meaning. Key ideas include Vectors and types, Components & magnitude, Dot (scalar) product, Cross (vector) product, Section formula.
What does Class 12 Mathematics Chapter 10 (Vector Algebra) cover on XamBaaz?+
It covers 66 NCERT-aligned MCQs on "Vector Algebra" — 22 Easy, 22 Medium and 22 Hard — each with a timed quiz and an instant explanation, suitable for CBSE Board exams, JEE Main and JEE Advanced.
Are these "Vector Algebra" questions free to practise?+
Yes — sign in with Google to practise "Vector Algebra" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Vector Algebra" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
Practise all 66 questions free
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