Vectors in 3D space – sum, dot product, angle

MathematicsVectors & Coordinate GeometryAges 17–18

An Oxyz coordinate system rotates with the mouse or a finger, showing two vectors u and v with given coordinates. The simulation draws the coordinate box of each vector and the parallelogram for the sum u + v, and computes lengths, the dot product u·v = x₁x₂ + y₁y₂ + z₁z₂, and the angle between the vectors; drag the coordinate sliders to see when u ⊥ v or when they point the same way.