Direction of dipole moment?

Question

Why is the direction of dipole moment taken from negative to positive charge when the field is directed in the opposite direction ?

Answer 1

It actually does not matter as long as you keep track of the signs. It was probably defined this way in order to give a similar formulation for torque

$$\vec{\tau} = \vec{r}\times\vec{F}$$

dipole moment is defined as $\vec{p} = q\vec{d}$ and torque on a dipole

$$\vec{\tau} = \vec{p}\times\vec{E}$$

If it was defined otherwise you had to write it down like $\vec{\tau} = \vec{E}\times\vec{p}$