Step by step
The question
Question: find the dot product of u = ⟨1, 2⟩ and v = ⟨3, 5⟩.
u = ⟨1, 2⟩ and v = ⟨3, 5⟩
1 Multiply the matching parts
The dot product: across times across, plus up times up.
u • v = 1 × 3 + 2 × 5
1 times 3 is 3.
2 times 5 is 10.
u • v = 3 + 10
3 plus 10 is 13.
So u • v = 13.
u • v = 13
Careful!
The dot product is not a vector.
We add the two products.
The answer is one number.
Careful: not ⟨3, 10⟩ ✗
2 Check
Does it make sense?
Let's draw u and v.
The angle between them is less than a square corner.
A positive dot product means the angle is less than 90°.
13 is positive.
It fits!
13 > 0 → less than 90°
Let's look back.
First: multiply the matching parts.
Last: check.
Answer
Careful: not ⟨3, 10⟩ ✗