Can the Differential Pass in the Beginning Part of a Change in Vector Product?

[Andrea Vironda]

Hi,
In a demostration i found a change in order i can't understand.
how can the differential pass in the beginning part? the only thing I'm sure is that "v" and "dr" are parallel

 

[jedishrfu]

There's a vector identity:

                                    | A1 A2 A3 |
A o B x C = B o C x A = C o A x B = | B1 B2 B3 |
                                    | C1 C2 C3 |

where 'o' is the dot product and 'x' is the cross product

more are here:

https://en.wikipedia.org/wiki/Vector_calculus_identities