why is very small angular displacement a vector quantity?How can we prove it?

Dear student,

Angular displacements, unlike linear displacements, do not commute with each other(which is, otherwise, an important property of vectors). Hence it cannot be technically classified as a vector. However infinitesimal angular displacements commute due to approximations into infinitesimal linear displacements. Henceinfinitesimal angular displacements are classified as vectors.