Page 2: Cartesian Representation and Vector Addition

This page explores how vectors are represented in the Cartesian coordinate system and introduces vector addition methods. The Pythagorean theorem is applied to calculate vector magnitudes.

Example: The magnitude of a vector can be calculated using the formula |v| = √(vx² + vy²), where vx and vy are the vector's components.

Definition: The parallelogram rule for vector addition involves drawing parallel lines to create a parallelogram, with the diagonal representing the resultant vector.

Highlight: Vector components are found by projecting the vector onto the coordinate axes.

Page 5: Practical Exercises

This page provides practical examples of vector operations, particularly focusing on velocity vectors and force diagrams.

Example: A problem involving two velocity vectors: v1 = 80 km/h and v2 = 30 km/h, demonstrating both parallelogram and tip-to-tail methods.

Highlight: Multiple solution methods are shown for the same problem to reinforce understanding.

Page 1: Vector Fundamentals

This page introduces the fundamental concepts of vectors and scalar quantities in physics. The distinction between scalar and vector quantities is clearly explained, with vectors being characterized by four essential properties.

Definition: A vector quantity is defined by its magnitude (modulo), direction, orientation (verso), and point of application.

Vocabulary:

• Modulo: The magnitude or size of the vector
• Direzione: The line along which the vector lies
• Verso: The orientation or sense of the vector
• Punto di applicazione: The starting point or tail of the vector

Highlight: Vectors are represented as arrows with a tail (starting point) and head (endpoint), with a special notation using an arrow above the symbol.