# Math – Find a quaternion of rotation from an orthonormal basis?

Given three unitary 3D vectors $$a$$, $$b$$, $$c$$ such as:

$$a times b = c$$

$$b times c = a$$

$$c times a = b$$

(that is to say $$a, b, c$$ for men orthonormal basis)

How do you calculate a unit quartile $$q$$ so that the product of the sand width (i.e. rotation) of $$q$$ the (1,0,0) is $$a$$, (0,1,0) is $$b$$ and (0,0,1) is $$c$$ ?