Step by step
The question
Question: find u + v, when u = ⟨2, −3⟩ and v = ⟨−2, 1⟩.
u = ⟨2, −3⟩ and v = ⟨−2, 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 = ⟨2 + (−2), −3 + 1⟩
Adding a negative is the same as taking away.
+ (−) = −
2 plus (−2) is 0.
−3 plus 1 is −2.
So u + v = ⟨0, −2⟩.
u + v = ⟨0, −2⟩
3 Check
Let's check on the grid.
The red arrow ends at (0, −2).
That is down 2 from the start: ⟨0, −2⟩.
The same!
tip (0, −2) → ⟨0, −2⟩
Let's look back.
First: draw tip to tail.
Then: add the parts.
Last: check.
Answer
u + v = ⟨0, −2⟩