This is something that has been bugging me since I started studying again. It seems to me that the definitions and symbols for the dot and cross products are backwards.
When I first learnt multiplication at school it was with the symbol 'x' as in times tables and all that. This is the symbol I'm most familiar with for multiplication as is the majority of people. When I was in the last years of high school studying mechanics I was introduced to dot products and cross products. The dot product is the same as the multiplication I have always done but has a different symbol. The cross product is a new special type of multiplication that uses the 'x' symbol I was used to for multiplying numbers.
I am used to using the 'x' to multiplying numbers - it would confuse me and most people that looked at my notes if I started putting the dot symbol in instead, so I would rather not.
Why isn't the operation known as the dot product denoted with the classic 'x' symbol and the new symbol used for the thing known as the cross product.
I have studied maths to high school level - carrying on till I was 18. I don't see myself studying to a higher level - I have almost reached the level of maths I can understand. I would appreciate if someone could explain to me if I am right in feeling this convention of notation is backwards or there is some logic to it I am missing that can be explained to me that aren't going to fly over my head.
EDIT: A follow up question. One way I thought of to avoid confusion was using the upside down V symbol for cross products. Is that opening up a new worms due to conflict with other uses of that symbol?
2nd Edit: I don't understand any of the other questions on the frontpage - i have come to the right place with people who do extreme mathematics