A vector equation is a mathematical expression that represents a vector in terms of its components. It typically takes the form r(t) = r₀ + t*v, where r(t) is the position vector, r₀ is a known point, t is a scalar parameter, and v is a direction vector. This equation describes a line in space, showing how the position changes as t varies. Vector equations are commonly used in physics and engineering to model motion and forces. They help in visualizing and solving problems related to trajectories, such as the path of a projectile or the movement of an object in a field. Understanding vector equations is essential for fields like calculus, physics, and computer graphics.