Scalar Product and Angle Between Vectors

This GeoGebra applet demonstrates the geometric interpretation of the dot product (scalar product) between two vectors and its relationship with the included angle. Users can interactively adjust vector components through input boxes to observe how the dot product changes and verify the formula a·b=|a||b|cosθ. Key mathematical concepts include vector coordinates in 3D space, dot product calculation, angle between vectors, and the law of cosines. Construction details: Textfield command creates interactive input boxes (inputBoxA_x, inputBoxA_y, inputBoxA_z, inputBoxB_x, inputBoxB_y, inputBoxB_z) for vector endpoints A, B, C; coordinate objects (A_x, A_y, A_z, B_x, B_y, B_z, C_x, C_y, C_z) define vectors; vector objects w and a represent computed vectors; text objects dynamically display the angle and calculation results. Suitable for high school mathematics courses on vectors and introductory linear algebra lessons.