Step by step
The question
Question: find u + v, when u = ⟨2, 3⟩ and v = ⟨4, −1⟩.
u = ⟨2, 3⟩ and v = ⟨4, −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 + 4, 3 + (−1)⟩
Adding a negative is the same as taking away.
+ (−) = −
2 plus 4 is 6.
3 plus (−1) is 2.
So u + v = ⟨6, 2⟩.
u + v = ⟨6, 2⟩
3 Check
Let's check on the grid.
The red arrow ends at (6, 2).
That is right 6 and up 2 from the start: ⟨6, 2⟩.
The same!
tip (6, 2) → ⟨6, 2⟩
Let's look back.
First: draw tip to tail.
Then: add the parts.
Last: check.
Answer
u + v = ⟨6, 2⟩