TITLE: What is the origin of unit vector notation? (i,j,k)
QUESTION [6 upvotes]: What is the origin of this notation? Who coined them and for what purpose?

REPLY [5 votes]: Maybe it originates from Hamilton's quaternions $\mathbb{H}$, which has a basis $1,i,j,k$ as a real vector space, and the multiplications there, namely, $i\cdot j=k, j\cdot k=i, k\cdot i=j$  correspond exactly to the wedge product in $\mathbb{R}^3$. So $\mathbb{R}^3$ can be viewed as the imanginary part of $\mathbb{H}$.
Anyway, this is just my understanding or my guess.