It's true by definition, there's really nothing more to it than that.

Angular velocity does not have to be represented by a vector, though it can be in 3 dimensions. We choose to represent it by the vector

$\vec{w} = \vec{r} \times \vec{v}$

And therefore following the cyclic properties of any cross product, it must be true that

$\vec{v} = \vec{w} \times \vec{r}$

It's true by definition, there's really nothing more to it than that.

Angular velocity does not have to be represented by a vector, though it can be in 3 dimensions. We choose to represent it by the vector

$$\vec{w} = \vec{r} \times \vec{v}\tag1$$

And therefore following the cyclic properties of any cross-product, it must be true that

$$\vec{v} = \vec{w} \times \vec{r}\tag2$$

It's true by definition, there's really nothing more to it by that.

Angular velocity does not have to be represented by a vector, though it can be in 3 dimensions. We choose to represent it by the vector

$\vec{w} = \vec{r} \times \vec{v}$

And therefore following the cyclic properties of any cross product, it must be true that

$\vec{v} = \vec{w} \times \vec{r}$

It's true by definition, there's really nothing more to it than that.

Angular velocity does not have to be represented by a vector, though it can be in 3 dimensions. We choose to represent it by the vector

$\vec{w} = \vec{r} \times \vec{v}$

And therefore following the cyclic properties of any cross product, it must be true that

$\vec{v} = \vec{w} \times \vec{r}$