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Applications of Vector Algebra

Tamil Nadu Board · Class 12 · Mathematics

Quick revision notes for Applications of Vector Algebra — Tamil Nadu Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions24 flashcards5 concepts

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Key Topics to Revise

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.

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Key Concepts

For vectorsFor vectorsThree vectorsA line passing through pointThe non

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 Applications of Vector Algebra — Chapter Overview Mind Map, Mind map showing all major topics covered in the Applications of Vector Algebra chapter, Flowchart showing the two equivalent methods for computing scalar triple product. These are the concepts Tamil Nadu Board Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Applications of Vector Algebra — Tamil Nadu Board Class 12 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and 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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All 12 chapters — Tamil Nadu Board Class 12 Mathematics Revision Notes

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