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Subtraction of Vectors


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 


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 $u-v$uv, 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. 






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