Vector Addition Explained: Graphical Representation in 2D Space #1814252 (License: Personal Use)

The image displays the geometric addition of two 2D vectors **a** and **b** using the head-to-tail (or parallelogram) method on a Cartesian plane. Components are explicitly labeled: **a** starts at origin and ends at (a₁, a₂); **b** starts at origin and ends at (b₁, b₂); their sum **a + b** extends from origin to (a₁+b₁, a₂+b₂). Dashed lines highlight the rectangular decomposition of each vector into x- and y-components.

Used in physics, engineering, and mathematics education to teach vector operations; commonly appears in textbooks, online tutorials, or lecture slides explaining linear algebra fundamentals or kinematics.