Vectors

Definition of a Vector

• A vector is a quantity that has both magnitude (size) and direction.
• Represented using bold letters (e.g., R) or with an arrow above the symbol ($\vec{R}$).

1. Adding and Subtracting Vectors

Graphical Method

• Vectors can be added or subtracted graphically by placing them head-to-tail.
• The resultant vector is the direct path from the start to the end.

2. Resolving Vectors into Components

Component Form

• A vector can be broken down into its horizontal ($\vec{R}_x$) and vertical ($\vec{R}_y$) components.
• These components are found using trigonometry:
  • $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} \Rightarrow R_x = R \cos \theta$
  • $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} \Rightarrow R_y = R \sin \theta$

---