Vector Components on Rotated Axes

This example demonstrates how a single vector’s components change when the coordinate axes rotate. It visually connects the rotation angle with the geometric decomposition of the vector into components along the rotated directions. Key concepts include vector representation, decomposition into components, and the projection-like geometric construction driven by right angles and the angle between the original and rotated axes. Construction-wise, it uses Intersect and Point to locate key intersections, Segment and Ray to build directional elements, OrthogonalLine to enforce perpendicular projections for the component decomposition, Angle to mark the rotation angle (α), and Vector to create the original vector and its components along the rotated axes defined by the constructed lines/objects. Suitable for middle and high school vector/geometry instruction and for introductory coordinate-geometry explorations.