Question: If a rigid body moves along a curve \(\alpha(s)\) (which we suppose is unit speed), and the motion of the body consists of translation along \(\alpha\) and rotation about \(\alpha\). The rotation is determined by an angular velocity vector \(\omega\) which satisfies \(T^{\prime}=\omega \times T, N^{\prime}=\omega \times N\) and w \(=\omega \times B\). The vector \(\omega\) is called the Darboux vector. Show that \(\omega\), in terms of \(T\), \(N\) and \(B\), to determine \(a\), \(b\) and \(c\).

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