Step by step
The question
Question: find the dot product of u = ⟨2, 0⟩ and v = ⟨4, 3⟩.
u = ⟨2, 0⟩ and v = ⟨4, 3⟩
1 Multiply the matching parts
The dot product: across times across, plus up times up.
u • v = 2 × 4 + 0 × 3
2 times 4 is 8.
0 times 3 is 0.
u • v = 8 + 0
8 plus 0 is 8.
So u • v = 8.
u • v = 8
Careful!
The dot product is not a vector.
We add the two products.
The answer is one number.
Careful: not ⟨8, 0⟩ ✗
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°.
8 is positive.
It fits!
8 > 0 → less than 90°
Let's look back.
First: multiply the matching parts.
Last: check.
Answer
Careful: not ⟨8, 0⟩ ✗