Lesson video

Hi, I'm Miss Davies.

In this lesson, we're going to be adding and subtracting column vectors to give a resultant vector.

What is the column vector that is shown on the diagram? It moves two to the right and five up.

This means that the vector is two, five.

What about this one? This vector travels four to the right and one up.

So this vector is four, one.

Let's work out two, five add four, one.

In total, this moves six to the right and six up Two, add four is six.

And five add one is six.

Let's have ago at this one.

Two, five subtract four, one.

This needs to go in the opposite direction.

As we are taking it away.

This time it goes two, to the left, which we write as negative two and four up Two subtract four is negative two, five subtract one is four.

Let's write down each of these lines as a column vector.

A, B Moves three to the right and four units up.

This is written as the vector.

Three, four.

The line segment B C is five to the right and two units down.

This is written as the vector five negative two, the line segment, A, C moves eight units to the right and two units up.

This is written after the vector eight two.

We are now going to add together the vectors, A, B and B, C.

This gives us a movement of eight squares to the right two units up.

Which is the vector eight two.

What do you notice? A, B add B, C is the same as A, C.

He asked me some questions for you to try.

Pause the video to complete your task, and resume once you're finished.

Here are the answers.

The arrows on the diagram show the direction of the vector.

The same as the arrows in the question today.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

The first diagram shows S subtract T.

The second diagram, choose the vector T subtract S.

The third diagram shows the vector S add T.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers Compare your answers to part D and G, E and H and F and I, what do you notice? The digits are the same.

Only one of them has positive values and one of them has negative values.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

Part A can be written as X add Y or Y add X.

And Part D can be written as X add Z or z add X.

This is because addition is commutative.

That's all for this lesson, thanks for watching.