Is there any entity similar to vectors but also possess the starting and ending points ?
For instance, consider a plane $z = 4$, Suppose I want a vector starting from A$(0,0,4)$ and ending at B$(0,1,4)$ with origin O$(0,0,0)$ how do I represent this? / What entity possess this information?
Until now I was in a state that vector also contains the information of starting and ending points, and tried to calculate the vector $\vec{AB}$ by calculating $\vec{OB} - \vec{OA}$, the answer I got is $(0,1,0)$ which is parallel to the vector $\vec{AB}$ I thought of , it is then I recalled vectors only have magnitude and direction.
So is there any such entity?
Edit : I meant to ask a $3D$ entity so that if it exists, the algebra with this will be helpful and easier.
Edit : So, after a decent search, I encountered grassmann algebra, which states that if I take the wedge product of a point with a vector I can have bound vector, which is what I exactly wanted.
So, what I want to know now is, Is there anything similar to bound vector in 3D vector algebra?
Actually there is.
The thing you are looking for stores information about starting and ending point of an applied vector, i.e. two points in $\mathbb R^3$. An ordered couple of points in $\mathbb R^3$ can be identified with a point in $\mathbb R^6$ in the following way:
$$A=(a_1,a_2,a_3);B=(b_1,b_2,b_3) \to (a_1,a_2,a_3,b_1,b_2,b_3)$$
So the thing you are looking for is actually a vector. Simply, in a bigger dimensional vector space.