Step by step
The question
Question: find u + v, when u = ⟨−3, 2⟩ and v = ⟨2, −3⟩.
u = ⟨−3, 2⟩ and v = ⟨2, −3⟩
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 = ⟨−3 + 2, 2 + (−3)⟩
Adding a negative is the same as taking away.
+ (−) = −
−3 plus 2 is −1.
2 plus (−3) is −1.
So u + v = ⟨−1, −1⟩.
u + v = ⟨−1, −1⟩
3 Check
Let's check on the grid.
The red arrow ends at (−1, −1).
That is left 1 and down 1 from the start: ⟨−1, −1⟩.
The same!
tip (−1, −1) → ⟨−1, −1⟩
Let's look back.
First: draw tip to tail.
Then: add the parts.
Last: check.
Answer
u + v = ⟨−1, −1⟩