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Maths

Vectors - Higher

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# Vector 'arithmetic'

## Equal vectors

If two vectors have the same magnitude and direction, then they are equal.

Look at the graph below to see the movements between PQ, QR and PR.

Vector followed by vector represents a movement from P to R.

Written out the vector addition looks like this

## Subtracting vectors

Subtracting a vector is the same as adding a negative version of the vector (remember that making a vector negative means reversing its direction).

Look at the diagram and imagine going from X to Z. How would you write the path in vectors using only the vectors and ?

You could say it is vector followed by a backwards movement along .

So we can write the path from X to Z as

Written out in numbers it looks like this:

Question

If x = , y = and z = , find:

1. -y
2. x - y
3. 2x + 3z

1. (Did you remember to change the signs?)

## Resultant vectors

To travel from X to Z, it is possible to move along vector followed by . It is also possible to go directly along .

is therefore known as the resultant of and .

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