Laws of Vector Addition: The Parallelogram Rule
🎯 Learning Objectives
- Understand what vectors are and how they differ from scalars
- Master the Parallelogram Law of vector addition
- Connect the Parallelogram Rule to the Triangle Rule
- Calculate the magnitude and direction of resultant vectors
1. What is a Vector?
A vector is a mathematical object that has both magnitude (size/length) and direction. We denote vectors as $\vec{a}$, $\vec{b}$, or in bold as a, b.
Examples of Vectors:
- Force: 10 N to the right
- Velocity: 60 km/h heading north
- Displacement: 5 m at 30° above horizontal
Scalars (NOT vectors):
- Temperature: 25°C
- Mass: 10 kg
- Speed: 60 km/h (no direction!)
When we add vectors, we combine their effects. This is fundamentally different from adding ordinary numbers because direction matters.