Linear Algebra & Vectors

Understand horizontal and vertical vector coordinate additions.

A **vector** represents a direction and magnitude in coordinate space. In a 2D grid, a vector is described by its horizontal component **(x)** and vertical component **(y)**. - **Vector Addition** combines two vectors $\vec{A}$ and $\vec{B}$ into a single resultant vector $\vec{R} = \vec{A} + \vec{B}$. - Geometrically, we perform this by moving Vector $\vec{B}$ to start from the tip of Vector $\vec{A}$ (the **tip-to-tail** method).

Vector A

Ax: 4

Ay: 3

Vector B

Bx: -2

By: 3

Vector A (Red): [4, 3]

Vector B (Blue): [-2, 3]

Resultant A + B: [2, 6]

Vector Math Basics

Component Addition: R = A + B = [Ax + Bx, Ay + By]
Vector Magnitude (Length): |A| = sqrt(Ax² + Ay²)
Vector Angle (Direction): θ = atan2(Ay, Ax)