## How can we use vectors to interpret geometry?

### Key questions

1. 1

What is a vector quantity and how is it different from a scalar quantity?

2. 2

What are the unit vectors $\mathbf{i},\mathbf{j},\mathbf{k}$?

3. 3

How can we use vectors to define lines?

4. 4

How can vectors help us to tackle geometric problems?

5. 5

How can we use vectors in mechanics?

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#### Introducing...

Resource type Title
Building blocks Hit the spot
Fluency exercise Vector squares
Many ways problem Make it equal

#### Developing...

Resource type Title
Rich example A frictional story
Building blocks Three lines
Fluency exercise Lots of vector lines!
Many ways problem Make it stop!
Food for thought One windy day
Food for thought Where did it land?

#### Review questions

Title Ref
Can we show that $OAQY$ is a parallelogram? R8704
Can we find the position vector of the intersection from the given ratios? R6007
Can we show the centre of mass moves in a straight line? R6491
Given the position of a mass, can we find its velocity and acceleration? R7678
How are these connected particles held on a slope? R8335
How can we show that $P, Q$ and $R$ are collinear? R9575
How fast do these connected particles move? R7982
If $A$, $P$ and $B$ are collinear, what's the value of $\lambda$? R7285
If $ABCDEFGH$ is a regular octagon, what do these vectors add to? R5992
If $C$ is on this line, can we find the ratio $AC:CB$? R5153
If $PRBQ$ is a parallelogram, what is the position vector of $Q$? R8573
If $Z$ is on $OA$ and also on $BY$, what is its position vector? R8798
If a disc is missing two smaller discs, where’s its centre of gravity? R6670
In a $\quantity{60}{km/h}$ wind, what bearing should this plane take? R6009
What if we join the midpoints of opposite sides of a quadrilateral? R8339
What is the position vector of $D$ if $ABCD$ is a parallelogram? R8215
When are these vectors parallel/perpendicular/the same length? R9629
Which direction should we steer to reach Rome? R8115