Vector understanding (basic)

Question

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

Answer 1

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.

Answer 2

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.