Lesson

Subtracting vectors combines the ideas of negative vectors and addition.

Remember how a negative vector has same size but opposite direction, well this means that the concept of subtracting a vector is the same as adding its negative.

That is that

$a-b=a+(-b)$`a`−`b`=`a`+(−`b`)

Geometrically it looks like this

here are vectors $u$`u` and $v$`v`

$u+v$`u`+`v` will look like this (remember to head to tail it)

$-v$−`v` will look like this, (same size as $v$`v`, just opposite direction)

and hence $u-v$`u`−`v`, or $u+-v$`u`+−`v` will look like this

Here are both situations to compare on the one diagram

Of course if we use matrix notation, then this becomes a simple process of matrix subtraction.

This applet will allow you to practice making vectors, and then demonstrate their subtraction via a geometric representation.