Step by step
The question
Question: find u − v, when u = ⟨3, −2⟩ and v = ⟨−1, 4⟩.
u = ⟨3, −2⟩ and v = ⟨−1, 4⟩
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 = ⟨3 − (−1), −2 − 4⟩
Taking away a negative is the same as adding.
− (−) = +
Careful!
Minus a negative is plus.
3 minus (−1) is 3 plus 1.
Careful: not 3 − (−1) = 2 ✗
3 minus (−1) is 4.
−2 minus 4 is −6.
So u − v = ⟨4, −6⟩.
u − v = ⟨4, −6⟩
3 Check
Let's check on the grid.
The red arrow ends at (4, −6).
That is right 4 and down 6 from the start: ⟨4, −6⟩.
The same!
tip (4, −6) → ⟨4, −6⟩
Let's look back.
First: draw tip to tail.
Then: take away the parts.
Last: check.
Answer
u − v = ⟨4, −6⟩