Step by step
The question
Question: find u − v, when u = ⟨2, 5⟩ and v = ⟨3, 2⟩.
u = ⟨2, 5⟩ and v = ⟨3, 2⟩
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 = ⟨2 − 3, 5 − 2⟩
2 minus 3 is −1.
5 minus 2 is 3.
So u − v = ⟨−1, 3⟩.
u − v = ⟨−1, 3⟩
3 Check
Let's check on the grid.
The red arrow ends at (−1, 3).
That is left 1 and up 3 from the start: ⟨−1, 3⟩.
The same!
tip (−1, 3) → ⟨−1, 3⟩
Let's look back.
First: draw tip to tail.
Then: take away the parts.
Last: check.
Answer
u − v = ⟨−1, 3⟩