Dot product of (1, 2, 3) and (4, -5, 6)

Step by step

The question

Question: find the dot product of (1, 2, 3) and (4, −5, 6).

The dot product u dot v: multiply matching entries, top with top and so on.

Then add them all.

The answer is one number.

1 Multiply matching entries

1 × 4 + 2 × (−5) + 3 × 6.

We work out each times.

2 Add them

Then we add: u • v = 12.

Careful!

The dot product is one number, not a vector.

The products are added together.

3 Check

Let's check the other way round: v dot u.

The same products, so the same number.

We get 12 again.

So the answer is right!

Let's look back.

First: multiply matching entries.

Then: add them.

Last: check.