Step by step
The question
Question: find u − v, when u = ⟨4, 1⟩ and v = ⟨1, 3⟩.
u = ⟨4, 1⟩ and v = ⟨1, 3⟩
1 Draw tip to tail
Draw the grid.
Draw u from the origin.
Taking away v is adding −v: the arrow turned around.
Put the start of −v at the tip of u.
Tip to tail.
The answer goes from the very start to the very end.
2 Take away the parts
Take away the across parts, and the up parts.
Taking away an arrow turns it around, so its parts change sign.
u − v = ⟨4 − 1, 1 − 3⟩
4 minus 1 is 3.
1 minus 3 is −2.
So u − v = ⟨3, −2⟩.
u − v = ⟨3, −2⟩
3 Check
Let's check on the grid.
The red arrow ends at (3, −2).
That is right 3 and down 2 from the start: ⟨3, −2⟩.
The same!
tip (3, −2) → ⟨3, −2⟩
Let's look back.
First: draw tip to tail.
Then: take away the parts.
Last: check.
Answer
u − v = ⟨3, −2⟩