**Exploring Vector Formulas: A Comprehensive Guide**

Vectors are a fundamental concept in mathematics, providing a powerful tool to represent quantities with both magnitude and direction. In this comprehensive guide, we will delve into various vector formulas, explore their applications, and work through solved examples to deepen your understanding.

Table of Contents

**Vector Basics:**

Before diving into formulas, let’s review some vector basics.

**2. Vector Addition and Subtraction**

**Addition:** The sum of two vectors **v** and **u** is calculated by adding corresponding components:

**3. Scalar Multiplication**

**Multiplication by a Scalar:** Scaling a vector **v** by a scalar c involves multiplying each component