📚 Key Concepts
Vector Definition- Quantity with magnitude and direction
- Position vectors
- Unit vectors î, ĵ, k̂
- Zero vector
Vector Types- Collinear vectors
- Coplanar vectors
- Equal vectors
- Unit vectors
- Position vectors
🎯 Key Formulas
Vector Operations:- Addition: Triangle/Parallelogram law
- Scalar multiplication: |ka| = |k||a|
- Dot product: a·b = |a||b|cosθ
- Cross product: |a×b| = |a||b|sinθ
- Component form: a = aₓî + a𝒚ĵ + aₖk̂
Direction Cosines:- cos α = l = x/|r|
- cos β = m = y/|r|
- cos γ = n = z/|r|
- l² + m² + n² = 1
⚠️ Common Mistakes to Avoid
Wrong direction in cross productConfusing dot and cross productIncorrect component resolutionVector addition errorsDirection cosine sign errorsUnit vector normalization
📖 Knowledge Prerequisites
Coordinate geometryTrigonometryBasic algebra3D visualizationVector components
💡 Tips for Students
Visualize vectors when possiblePractice right-hand rule for cross productRemember dot product propertiesMaster component form calculationsLearn standard vector operationsUse proper vector notation
👉 Practice Recommedations
Basic vector operationsFinding unit vectorsDot product applicationsCross product problemsDirection cosines/ratiosVector algebra proofsGeometric applications
Practice each question with a timer and get instant feedback
.svg){kind=small}