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Grade 12

Subtraction of Vectors

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 

$a-b=a+(-b)$ab=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 $u-v$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. 

 

 

 

 

 

Outcomes

12CT.D.1.5

Determine, through investigation using a variety of tools (e.g., graph paper, technology) and strategies (i.e., head-to-tail method; parallelogram method; resolving vectors into their vertical and horizontal components), the sum (i.e., resultant) or difference of two vectors

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