how a vector's components transform between two different orthonormal bases related by a rotation

This interactive web tool that demonstrates how a vector's components change when viewed from two different orthonormal bases that are related by a rotation. The user can adjust the rotation angle between a standard basis and a rotated basis, as well as define a vector by its components. The visualization will then draw the vector and use dashed lines to show its components projected onto both sets of axes. The demo will also calculate and display the vector's new components in the rotated basis, visually confirming the underlying transformation equations.

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