Step by step
The question
Question: find u + v, when u = ⟨1, 2⟩ and v = ⟨3, 1⟩.
u = ⟨1, 2⟩ and v = ⟨3, 1⟩
1 Draw tip to tail
Draw the grid.
Draw u from the origin.
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 Add the parts
Add the across parts, and the up parts.
Each arrow adds its own across and up.
u + v = ⟨1 + 3, 2 + 1⟩
1 plus 3 is 4.
2 plus 1 is 3.
So u + v = ⟨4, 3⟩.
u + v = ⟨4, 3⟩
3 Check
Let's check on the grid.
The red arrow ends at (4, 3).
That is right 4 and up 3 from the start: ⟨4, 3⟩.
The same!
tip (4, 3) → ⟨4, 3⟩
Let's look back.
First: draw tip to tail.
Then: add the parts.
Last: check.
Answer
u + v = ⟨4, 3⟩