Step by step
The question
Question: find u − v, when u = ⟨1, 4⟩ and v = ⟨5, 2⟩.
u = ⟨1, 4⟩ and v = ⟨5, 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 = ⟨1 − 5, 4 − 2⟩
1 minus 5 is −4.
4 minus 2 is 2.
So u − v = ⟨−4, 2⟩.
u − v = ⟨−4, 2⟩
3 Check
Let's check on the grid.
The red arrow ends at (−4, 2).
That is left 4 and up 2 from the start: ⟨−4, 2⟩.
The same!
tip (−4, 2) → ⟨−4, 2⟩
Let's look back.
First: draw tip to tail.
Then: take away the parts.
Last: check.
Answer
u − v = ⟨−4, 2⟩