Step by step
The question
Question: O A is the vector a and O B is the vector b: find the vector B A.
1 Find a route
We want to go from B to A.
We go along arrows we know: B O, then O A.
So B A is B O plus O A.
BA = BO + OA
2 Write it with a and b
Careful!
Going against the arrow is the opposite vector: it gets a minus.
Careful: not BO = b ✗
B O goes against the arrow b: minus b.
O A is a.
BA = −b + a
3 Collect the a and b
The a's together and the b's together: a minus b.
BA = a − b
a terms + a terms, b terms + b terms
4 Check
Let's check with numbers: a = (0, 4) and b = (6, 0).
Our answer gives (-6, 4): exactly the step from B to A.
So it is right!
a = (0, 4), b = (6, 0): BA = (-6, 4) = A(0, 4) − B(6, 0)
Let's look back.
First: find a route.
Then: write it with a and b.
Then: collect the a and b.
Last: check.
Answer
a terms + a terms, b terms + b terms