Dynamic 3D Vector Projection Demonstration

① This GeoGebra example dynamically demonstrates the projection of vector u onto vector v in three-dimensional space, visually showing the construction and length of the projected vector w. ② Core mathematical concepts include vector projection, dot product, vector length, cosine of the angle between vectors, and spatial relationships in 3D. ③ Construction highlights: uses Vector command to create vectors u and v, Length command to measure magnitudes, Segment command to construct the projection segment, Angle command to label the angle α; interactive buttons button1 and button2 control dynamic changes, with text boxes text1-text4 displaying numerical values; objects include points A, B, C and auxiliary vectors a, b, c, d, e, f, h, i, j, enabling exploratory learning. ④ Suitable for high school to early college students learning vector algebra and 3D geometry, and for teachers to demonstrate or students to investigate the projection formula interactively.