Most students skip the vectors question. Think of each vector as a bus route and every question becomes a journey you can plan.
Each letter is a route you know
O to A is route a. O to B is route b. You can only ride routes you already know.
How do you get from A to B?
There's no direct bus. So change at O: ride route a backwards, then ride route b.
Going backwards makes it negative, so A to B is −a + b. That's usually written AB = b − a.
That's the whole trick: no direct route? Go the long way round, through places you know.
Worked example: the midpoint
M is halfway along AB. What's OM?
Ride to A: that's a. Then go half of AB: ½(b − a). Add them and tidy up:
OM = a + ½b − ½a = ½a + ½b.
One thing to watch: vectors are named start first, then end. AB means from A to B, so BA = −AB.
N is halfway along OB. What's AN?
Show the answer
Ride a backwards to O (−a), then half of route b (½b). So AN = −a + ½b, which you can also write as ½b − a.
Save this for your next test
- Each vector is a route you know.
- No direct route? Go the long way round.
- Riding a route backwards makes it negative.
- AB means from A to B.
Read the video transcript
- Most students skip the vectors question. Here's the trick that makes it easy.
- Think of vectors as bus routes. Each letter is a route you already know.
- O to A is route a. O to B is route b.
- Now, how do you get from A to B? There's no direct bus.
- So change at O. Ride route a backwards, then ride route b.
- Going backwards makes it negative. So A to B is minus a, plus b.
- A B equals b minus a.
- That's the trick: no direct route? Go the long way round, through places you know.
- Let's try one. M is halfway along A B. What's O M?
- Ride to A: that's a. Then half of A B: a half of b minus a.
- Tidy it up: a half a, plus a half b.
- Now you: N is halfway along O B. What's A N? Tell me in the comments.
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