Step by step
The question
Question: find the dot product of u = ⟨3, 4⟩ and v = ⟨2, 1⟩.
u = ⟨3, 4⟩ and v = ⟨2, 1⟩
1 Multiply the matching parts
The dot product: across times across, plus up times up.
u • v = 3 × 2 + 4 × 1
3 times 2 is 6.
4 times 1 is 4.
u • v = 6 + 4
6 plus 4 is 10.
So u • v = 10.
u • v = 10
Careful!
The dot product is not a vector.
We add the two products.
The answer is one number.
Careful: not ⟨6, 4⟩ ✗
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°.
10 is positive.
It fits!
10 > 0 → less than 90°
Let's look back.
First: multiply the matching parts.
Last: check.
Answer
Careful: not ⟨6, 4⟩ ✗