What is the point of writing vectors in the i + j form?

Question

I don't get it. I mean I understand how the X i or j physically works (it's just factoring it basically), but WHY do it in the first place? To confuse me? To make me write more? WHY?!!? OH WHY!!?!?!?

Thnx, I'll pick a best answer TODAY, you silly willies.

Answer 1

The idea that a vector is a linear combination of certain fixed basis vectors has a LOT of utility. For one thing, one can use matrix algebra to manipulate coordinate systems based on that. This is a key idea in everything from electronic signal analysis to high-end commercial applications of statistics.

It's also useful to theoretical mathematicians and physicists in all sorts of ways.

Answer 2

It's for ease. Would you rather write <1,1> or a vector of magnitude sqrt(2) in the 45 degree direction?

As for why i and j are chosen, it's because they're unit vectors that are perpendicular to each other. It makes certain calculations easier, cross product being one of them.