Step by step
The question
Question: find 3v, when v = ⟨2, 1⟩.
v = ⟨2, 1⟩
1 Draw the arrows
Draw the grid.
Draw v = ⟨2, 1⟩ from the origin.
3v means 3 times v: 3 arrows v, tip to tail.
Together they make one arrow, 3 times as long.
That is 3v.
2 Multiply each part
3v means: multiply each part of v by 3.
3v = ⟨3 × 2, 3 × 1⟩
Careful!
Both parts are multiplied, not only the first one.
The arrow gets longer across and up.
Careful: not ⟨6, 1⟩ ✗
3 times 2 is 6.
3 times 1 is 3.
So 3v = ⟨6, 3⟩.
3v = ⟨6, 3⟩
3 Check
Let's check on the grid.
The red arrow ends at (6, 3).
That is right 6 and up 3 from the start: ⟨6, 3⟩.
The same!
tip (6, 3) → ⟨6, 3⟩
Let's look back.
First: draw the arrows.
Then: multiply each part.
Last: check.
Answer
3v = ⟨6, 3⟩