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