Vectors – sum, difference, scalar multiple and dot product

MathematicsVectors & Coordinate GeometryAges 15–16

Two vectors u, v are drawn from the origin O on a coordinate grid; students drag the tips of u and v (snapped to the grid) and pick an operation. The sum follows the parallelogram rule, the difference u − v joins the tip of v to the tip of u, the scalar multiple k·u stays parallel to u, and the dot product u·v = |u||v|cos(u, v) = x₁x₂ + y₁y₂ is shown with the angle and projection visible; coordinates and results update instantly.