Step by step
The question
Question: find −2v, when v = ⟨−1, 2⟩.
v = ⟨−1, 2⟩
1 Draw the arrows
Draw the grid.
Draw v = ⟨−1, 2⟩ from the origin.
A minus turns the arrow around: −v points the other way.
−2v is 2 times as long, turned around.
2 Multiply each part
−2v means: multiply each part of v by −2.
−2v = ⟨−2 × (−1), −2 × 2⟩
Careful!
Both parts are multiplied, not only the first one.
The arrow gets longer across and up.
Careful: not ⟨2, 2⟩ ✗
−2 times (−1) is 2.
−2 times 2 is −4.
So −2v = ⟨2, −4⟩.
−2v = ⟨2, −4⟩
3 Check
Let's check on the grid.
The red arrow ends at (2, −4).
That is right 2 and down 4 from the start: ⟨2, −4⟩.
The same!
tip (2, −4) → ⟨2, −4⟩
Let's look back.
First: draw the arrows.
Then: multiply each part.
Last: check.
Answer
−2v = ⟨2, −4⟩