Students represent vectors geometrically and in Cartesian components in two dimensions, and in three dimensions where appropriate, determining their magnitude, direction, and unit vector and multiplying them by real scalars. They add and subtract vectors, resolve them into perpendicular components, and use the dot product to determine alignment, perpendicularity, and the angle between nonzero vectors. They apply these skills to two-dimensional force, displacement, velocity, and acceleration problems, interpreting resultant vectors and recognizing equilibrium when the net force is zero.