Sometimes, vectors need to be subtracted rather than added. For example, if you are in a car moving at $2.0\,m\,{s^{ - 1}}$ and another car on the same road is moving in the same direction at $5.0\,m\,{s^{ - 1}}$, then you approach the car at $5.0 - 2.0 = 3.0\,m\,{s^{ - 1}}$. You are subtracting two velocity vectors.
Subtraction of vectors can be done using the formula:

$A − B = A + (− B)$

where A and B are vectors.

So, to subtract, just add the negative vector.
But first you have to understand what the negative of vector B means. The negative of vector B is another vector of the same size as B but in the opposite direction.
This is straightforward if the velocities are in the same direction. For example, to subtract a velocity of $4\,m\,{s^{ - 1}}$ north from a velocity of $10\,m\,{s^{ - 1}}$ north, you start by drawing a vector $10\,m\,{s^{ - 1}}$ north and then add a vector of 4 m s−1 south. The answer is $6\,m\,{s^{ - 1}}$ north.
It is less straightforward if the velocities are in the opposite direction. For example, to subtract a velocity of $4\,m\,{s^{ - 1}}$ south from a velocity of $10\,m\,{s^{ - 1}}$ north, you start by drawing a vector $10\,m\,{s^{ - 1}}$ north and then add a vector of $4\,m\,{s^{ - 1}}$ north. The answer is $14\,m\,{s^{ - 1}}$ north.
The example in Figure 1.17 shows how to find $A − B$ and $A + B$ when the vectors are along different directions.

Question

 

18) A velocity of $5.0\,m\,{s^{ - 1}}$ is due north. Subtract from this velocity another velocity that is:
a: $5.0\,m\,{s^{ - 1}}$ due south
b: $5.0\,m\,{s^{ - 1}}$ due north

c: $5.0\,m\,{s^{ - 1}}$ due west
d: $5.0\,m\,{s^{ - 1}}$ due east 
(You can do a scale drawing or make a calculation but remember to give the direction of your answers as well as their size.)