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Applications of Vector Algebra — Syllabus

Tamil Nadu Board · Class 12 · Mathematics

What Applications of Vector Algebra covers in Tamil Nadu Board Class 12 Mathematics: 4 topics, for the 2026-27 session.

45 questions24 flashcards4 formulas & key relations5 concepts

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4 Topics · Tamil Nadu Board Class 12 Mathematics · 2026-27

Topics in Applications of Vector Algebra

1

Scalar Product (Dot Product) and Vector Product (Cross Product) — Quick Recap

  • Dot product: a⃗ · b⃗ = a₁b₁ + a₂b₂ + a₃b₃ = |a⃗||b⃗|cosθ. Result is a SCALAR.
  • Cross product: a⃗ × b⃗ = determinant form with î, ĵ, k̂ in first row. Result is a VECTOR.
  • a⃗ · b⃗ = 0 ⟺ vectors are PERPENDICULAR (non-zero vectors).
2

Scalar Triple Product

  • Scalar triple product of a⃗, b⃗, c⃗ is defined as (a⃗ × b⃗) · c⃗ and is denoted as [a⃗, b⃗, c⃗].
  • Result is a SCALAR.
  • Formula: [a⃗, b⃗, c⃗] = |a₁ a₂ a₃ / b₁ b₂ b₃ / c₁ c₂ c₃| (3×3 determinant).
3

Vector Triple Product

  • Vector triple product of a⃗, b⃗, c⃗ is a⃗ × (b⃗ × c⃗). Result is a VECTOR.
  • Expansion formula: a⃗ × (b⃗ × c⃗) = (a⃗ · c⃗)b⃗ − (a⃗ · b⃗)c⃗.
  • Memory trick: 'BAC minus CAB rule' — a⃗ × (b⃗ × c⃗) = (a⃗·c⃗)b⃗ − (a⃗·b⃗)c⃗.
4

Equations of a Straight Line in 3D

  • Parametric vector form (through point a⃗, parallel to b⃗): r⃗ = a⃗ + tb⃗, t ∈ ℝ.
  • Non-parametric vector form: (r⃗ − a⃗) × b⃗ = 0⃗.
  • Cartesian form: (x−x₁)/b₁ = (y−y₁)/b₂ = (z−z₁)/b₃.

Key Concepts

For vectorsFor vectorsThree vectorsA line passing through pointThe non

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Frequently Asked Questions

What are the important topics in Applications of Vector Algebra for Tamil Nadu Board Class 12 Mathematics?
Key topics in Applications of Vector Algebra include Scalar Product (Dot Product) and Vector Product (Cross Product) — Quick Recap, Scalar Triple Product, Vector Triple Product, Equations of a Straight Line in 3D. Study these first, then practise questions on each for the Tamil Nadu Board Class 12 board exam.
How should I revise Applications of Vector Algebra for the Tamil Nadu Board Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Applications of Vector Algebra. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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