Step by step
The question
Question: find the dot product of u = ⟨5, 12⟩ and v = ⟨−2, 3⟩.
u = ⟨5, 12⟩ and v = ⟨−2, 3⟩
1 Multiply the matching parts
The dot product: across times across, plus up times up.
u • v = 5 × (−2) + 12 × 3
5 times (−2) is −10.
12 times 3 is 36.
u • v = −10 + 36
−10 plus 36 is 26.
So u • v = 26.
u • v = 26
Careful!
The dot product is not a vector.
We add the two products.
The answer is one number.
Careful: not ⟨−10, 36⟩ ✗
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°.
26 is positive.
It fits!
26 > 0 → less than 90°
Let's look back.
First: multiply the matching parts.
Last: check.
Answer
Careful: not ⟨−10, 36⟩ ✗