Vectors vs Scalars
Vectors have both magnitude (size) and direction, like velocity and force. Scalars only have magnitude, like temperature and mass. This distinction is crucial for understanding motion and forces.
Vector representation can be done three ways: using vector notation (A⃗), drawing rays with length proportional to magnitude, or using coordinates (x,y). The arrow's length shows magnitude, while its direction shows the vector's direction.
Displacement vs distance perfectly illustrates the vector-scalar difference. If you walk 25m to the cafeteria and back, your distance is 50m (scalar), but your displacement is 0m (vector) since you ended where you started.
Direction convention: Positive directions are typically North, East, forward, upward, and rightward. Negative directions are South, West, backward, downward, and leftward.