If I am right you can only do vector product for vectors. Here you have dipole moment $= q×d$. Then are we assuming charge is a vector? But how then does charge obey the triangle law of vector addition (,ie apart from having a direction a quantity must also obey the vector addition law). This is the reason why current isn't a vector. But I don't understand how we assume charge is a vector?
Another confusion I stumbled upon is, the direction of a vector product should be perpendicular to both the vectors. In this case, dipole moment is from negative to positive. Which is along the direction of the distance vector (distance vector? You mean position vector???)
I think I am missing out two things. How that vector product is even possible (having rejected the hypothesis of charge being a vector). And two what is the distance vector? What's it's direction. In nutshell, how do you describe both the "vectors"
Thanks in advance. Apologies if I made a typo. I am on mobile right now, leaving my lunch cold and annoyed that this formula $q×d$ even exists .
Edit: here's the picture since I feel it tells how I got confused