Step by step
The question
Question: find the dot product of (2, 0, 1) and (3, 4, 5).
u = [2; 0; 1], v = [3; 4; 5]
The dot product u dot v: multiply matching entries, top with top and so on.
Then add them all.
The answer is one number.
u • v: matching entries multiplied, then added
1 Multiply matching entries
2 × 3 + 0 × 4 + 1 × 5.
u • v = 2 × 3 + 0 × 4 + 1 × 5
We work out each times.
u • v = 6 + 0 + 5
2 Add them
Then we add: u • v = 11.
u • v = 11
Careful!
The dot product is one number, not a vector.
The products are added together.
Careful: one number, not a vector
3 Check
Let's check the other way round: v dot u.
The same products, so the same number.
v • u = 3 × 2 + 4 × 0 + 5 × 1 = 6 + 0 + 5 = 11
We get 11 again.
So the answer is right!
Let's look back.
First: multiply matching entries.
Then: add them.
Last: check.
Answer
Careful: one number, not a vector