Step by step
The question
Question: O A is the vector a and O B is the vector b, and N is the midpoint of O B: find the vector O N.
1 Find a route
We want to go from O to N.
We go along arrows we know: O N.
So O N is O N.
ON = ON
2 Write it with a and b
O N is half of O B: half b.
ON = 12b
3 Check
Let's check with numbers: a = (0, 4) and b = (6, 0).
Our answer gives (3, 0): exactly the step from O to N.
So it is right!
a = (0, 4), b = (6, 0): ON = (3, 0) = N(3, 0) − O(0, 0)
Let's look back.
First: find a route.
Then: write it with a and b.
Last: check.
Answer
ON = 12b