Vector Addition

Add vectors graphically and by components

Vectors have both magnitude and direction. Vector addition follows the parallelogram law (or tip-to-tail): place vectors head to tail and draw the resultant from start to end. Equivalently, add components separately: R_x = A_x + B_x, R_y = A_y + B_y. The magnitude and direction of the resultant follow from Pythagorean theorem and arctangent. This is the foundation for analyzing 2D forces, velocity, and displacement.