Dot product of (1, 2, -3, 4) and (2, 0, 1, -1)

Step by step

The question

Question: find the dot product of (1, 2, −3, 4) and (2, 0, 1, −1).

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 × 2 + 2 × 0 + (−3) × 1 + 4 × (−1).

We work out each times.

2 Add them

Then we add: u • v = −5.

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 −5 again.

So the answer is right!

Let's look back.

First: multiply matching entries.

Then: add them.

Last: check.