A vector equation is a mathematical expression that represents a vector in terms of its components. It typically takes the form v = ai + bj + ck, where v is the vector, and a, b, and c are its scalar components along the x, y, and z axes, respectively. This equation allows for the visualization and manipulation of vectors in a coordinate system. Vector equations are commonly used in physics and engineering to describe motion, forces, and other phenomena. They can also represent lines and planes in space, making them essential in fields like computer graphics and robotics. Understanding vector equations is crucial for solving problems involving direction and magnitude.