Step by step
The question
Question: find u + v, when u = ⟨1, 2, 3⟩ and v = ⟨4, 0, −1⟩.
u = ⟨1, 2, 3⟩, v = ⟨4, 0, −1⟩
1 Add part by part
Add the matching parts: x with x, y with y, z with z.
u + v = ⟨1 + 4, 2 + 0, 3 + (−1)⟩
So u + v = ⟨5, 2, 2⟩.
u + v = ⟨5, 2, 2⟩
2 Check
Let's check with a picture.
First u from the origin.
Then v from its tip.
The arrow from the start to the end is the answer.
Tip to tail: ⟨1, 2, 3⟩ then ⟨4, 0, −1⟩ ends at ⟨5, 2, 2⟩.
Right!
⟨1, 2, 3⟩ + ⟨4, 0, −1⟩ = ⟨5, 2, 2⟩
Let's look back.
First: add part by part.
Last: check.
Answer
u + v = ⟨5, 2, 2⟩