Step by step
The question
Question: find the vector from (1, 1) to (1, 6), and its length.
(1, 1) to (1, 6)
1 Draw the arrow
Draw the grid.
The arrow starts at (1, 1)
and ends at (1, 6).
Draw the arrow from the start to the end.
We call it v.
2 Count across and up
Both points have the same x.
We do not go across: 0.
Up: from y = 1 to y = 6 is up 5.
A vector is written with its two parts: across, then up.
Each part is end minus start.
v = ⟨1 − 1, 6 − 1⟩
end − start
Careful!
Not start minus end.
That gives ⟨0, −5⟩: an arrow pointing the other way.
Careful: not ⟨1 − 1, 1 − 6⟩ ✗
1 minus 1 is 0.
6 minus 1 is 5.
So v = ⟨0, 5⟩.
v = ⟨0, 5⟩
3 Find the length
The arrow goes straight up.
So its length is just 5.
‖v‖ = 5
4 Check
Let's check: start at (1, 1) and add the parts.
We land on (1, 6), the end!
(1 + 0, 1 + 5) = (1, 6)
Let's look back.
First: draw the arrow.
Then: count across and up.
Then: find the length.
Last: check.
Answer
v = ⟨0, 5⟩