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\mathbf{q}_2 = \mathbf{q}_y = \sin(\alpha/2)\cdot1\\
\mathbf{q}_3 = \mathbf{q}_z = \sin(\alpha/2)\cdot0\end{array}</math>
If the [[axis of rotation]] is the ''z''-axis:
:<math>\begin{array}{lcr} \mathbf{q}_0 = \mathbf{q}_w = \cos(\alpha/2)\\
\mathbf{q}_1 = \mathbf{q}_x = \sin(\alpha/2)\cdot0\\
\mathbf{q}_2 = \mathbf{q}_y = \sin(\alpha/2)\cdot0\\
\mathbf{q}_3 = \mathbf{q}_z = \sin(\alpha/2)\cdot1\end{array}</math>
If the [[axis of rotation]] is a [[Vector_(mathematics_and_physics)|vector]] located 45° ({{sfrac|{{pi}}|4}} radians) between the ''x'' and ''y'' axes:
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