# Vector understanding (basic)

Im new to vectors and i am confused about the notation.

Say you wanted to graphially represent a vector in two dimensional space i get that you can use a directed line segment and we can denote this as PQ with an arrow above.

Am i right in saying that the points P and Q have no relevance unless you are dealing with displacement vectors?

Is PQ with an arrow above notation ever used to represent say a velocity vector or would you just use a. Thanks

• I would agree to your sentiments that the PQ notation is only useful when you care about the endpoints, and that yes, for velocity vectors you don't care about the endpoints. Whether or not it is only useful for displacement vectors specifically is a completely different matter. Jan 14, 2019 at 15:04

The way I have always thought about it is that the points $$P$$ and $$Q$$ are used for defining the vector. I.e. it's direction and magnitude, but once the vector has been defined, you are then free to use it anywhere.
I can't recall having ever seen $$\overrightarrow{PQ}$$ used as a velocity and I am in my 3rd year of a maths degree.
$$\overrightarrow{PQ}$$ = \overrightarrow{PQ} with \$ signs around it.
In physics, there are cases when the start of the vector does not matter, and there are cases when it does. If you talk just equilibrium of the forces, you write a force as $$\vec F$$. This is equivalent to saying that the initial point is at the origin, so it's a shorthand for $$\vec {OF}$$. But sometimes the origin of the vector matters, like in the equilibrium of the torques. The way to get around that is to define two vectors. You write is as $$\vec r\times \vec F$$, where $$\vec r$$ tells you how much the force $$F$$ is displaced from the origin.