Step by step
The question
Question: find the vector from (2, 3) to (7, 3), and its length.
(2, 3) to (7, 3)
1 Draw the arrow
Draw the grid.
The arrow starts at (2, 3)
and ends at (7, 3).
Draw the arrow from the start to the end.
We call it v.
2 Count across and up
Across: from x = 2 to x = 7 is right 5.
Both points have the same y.
We do not go up or down: 0.
A vector is written with its two parts: across, then up.
Each part is end minus start.
v = ⟨7 − 2, 3 − 3⟩
end − start
Careful!
Not start minus end.
That gives ⟨−5, 0⟩: an arrow pointing the other way.
Careful: not ⟨2 − 7, 3 − 3⟩ ✗
7 minus 2 is 5.
3 minus 3 is 0.
So v = ⟨5, 0⟩.
v = ⟨5, 0⟩
3 Find the length
The arrow goes straight across.
So its length is just 5.
‖v‖ = 5
4 Check
Let's check: start at (2, 3) and add the parts.
We land on (7, 3), the end!
(2 + 5, 3 + 0) = (7, 3)
Let's look back.
First: draw the arrow.
Then: count across and up.
Then: find the length.
Last: check.
Answer
v = ⟨5, 0⟩