Let’s give a name to properties that are *collections* of numbers: let’s call them **vectors**.^{1}

Position is hereby a vector. We can call it the **position vector**, when we wish to emphasise that fact. Vectors somewhat feel like arrows, and we can draw a position as an arrow to the location.

Whenever you hear someone tell a position with only a number without also telling the direction – ‘where did they go? 10 more metres and you’ll find them!’ – the direction must be implied. This number itself is clearly just the “size” of the position, the ‘how far’ part. We could call it the **magnitude** of the vector, since it sort of feels like the length of that arrow we just drew.

Let’s invent an arrow symbol $\vec ~$ to symbolise a vector. We can simply add it to the $s$ symbol we already chose for position:^{2}

$s=5\,\mathrm{m}\quad$ and $\quad \vec s= \left(\begin{matrix}

3 \\

4 \\

\end{matrix}\right)\mathrm {m}$

The $s$ is a position, where the direction is implied. And the $\vec s$ is also a position. *Both *are positions. Obviously, position without its direction is exactly the same as *distance* or *length* $L$. This size property fully overlaps with $s$. So, you will often hear people refer to the magnitude of position as the *distance* or *length* of position. You might even hear people say: ‘position is a vector; distance/length is its magnitude’.

To ease our writing, let’s agree that coordinates can also be written horizontally if we need to – we’ll just have to separate them by something, for example a comma $,$ :^{3}

$(3,4)\,\mathrm{m}\quad$ and $\quad(3,4,5)\,\mathrm{m}$

We have now invented the fine word ‘vector’ for a property that is a collection of numbers. Similarly, a fine word for a property that is a *single *number also exists: it is called a **scalar**.^{[3,4,5]}

So,

- length/distance $L$, area $A$, volume $V$, time $t$, quantity $n$ and of course the direction-less position $s$ are scalars, carrying magnitude only, while
- $\vec s$ is a vector, carrying magnitude and direction.
^{4}

We will rarely use the word ‘scalar’, but you can easily encounter it in technical surroundings.

References:

- ‘
**Online Etymology Dictionary**’ (dictionary),*Douglas Harper*, www.etymonline.com - ‘
**Quantities and units -- Part 2: Mathematical signs and symbols to be used in the natural sciences and technology**’ (article), ISO 80000-2:2009, 1st ed., 2009, www.iso.org/standard/31887.html - ‘
**Scalars and Vectors**’ (web page), The Physic Classroom, www.physicsclassroom.com/class/1DKin/Lesson-1/Scalars-and-Vectors (accessed Sep. 12th, 2019) - ‘
**Scalar**’ (encyclopedia), Encyclopædia Britannica, 2009,__www.britannica.com/science/scalar__(accessed May 7th, 2019) - ‘
**Sears and Zemansky’s Univesity Physics with Modern Physics**’ (book),*Hugh D. Young & Roger A. Freedman*, Pearson Education, 13th ed., 2012