Subtracting vectors

Subtracting - Reverse

Reverse the direction of the vector you want to subtract

Example 1

Subtract vector $a$ from vector $b$

Take 2 vectors one with a height of 3 and the other a height of 2

Draw the vectors together as you were adding them

Place the first vector $a$ and add on the reverse of vector $b$

The result is a new vector $c$

Draw the first vector down completely so you can start to see a triangle

NOTE:

It doesn't matter in which order you subtract vectors or add vectors. Therefore:

$a-b=-b+a$

But try $-b+a$ and see for yourself.

But try `-b+a` and see for yourself.

$a-b=c$ and $-b+a=c$

Another way of showing $a-b=-b+a$ is as follows:

Example 2

Remember you can subtract and add vectors in any order as long as they join

$a-b=-b+a$

Connect a vector to the opposing corners then minus two of the sides

Example 3

You can connect any vectors up as long as they meet, but the parallel vector to the resultant vector needs to be negative

Vector $r=a-b+c+d$

Also

When subtracting vectors remember to turn the parallel vector to the resulting vector is negative

Vector $r=c+a-b+d$

You can add vectors and reversed vectors in any order.