Position Vectors in Component Form in 3D

This GeoGebra example demonstrates how a position vector in three-dimensional space is represented in component form, showing that the vector from the origin to a point has components equal to the point's coordinates. It visually links the algebraic components (x, y, z) to the geometric vector in a 3D coordinate system. The construction uses the Vector command to create the main vector v from the origin to point A, and the If command to conditionally display or hide components. Key objects include points A, B, C, i, j, k, the vector v, auxiliary segments, and text labels for annotations. This is suitable for high school or introductory college students learning about vectors, coordinate geometry, or spatial reasoning, and serves as an interactive teaching tool for understanding vector decomposition and coordinate representation.