Chapter 11 of 12
Revision Notes
Applications of Vector Algebra — Revision Notes
Tamil Nadu Board · Class 12 · Mathematics
Applications of Vector Algebra revision notes for Tamil Nadu Board Class 12 Mathematics: 4 topics in quick points.
45 questions24 flashcards4 formulas & key relations5 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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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 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.
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