Lesson video

Hi, I'm Miss Davies.

In this lesson, we're going to be working with the simple vector diagrams. The shape A, B, C, D is a parallelogram.

We're going to write the following vectors in terms of a and b.

A to B we can see from our diagram is a.

B to C is b.

B to A means we are starting at B and travelling to A is negative a, as it goes in the opposite direction to which the way that the arrow is pointing.

C to B is negative b.

D to C is a, as it is parallel and the same length as the vector a, it is AB.

We know this as it is a parallelogram.

C to D is negative a.

A to D is parallel to BC and an equal length so it is the vector b.

D to A is the opposite direction to AD, so it is negative b.

We're now going to write vector AC in terms of a and b.

AC starts at A and travels to C.

We can see from lines that are drawn onto the parallelogram that this is a add b.

C to A starts at C and travels to A.

These lines are in the opposite direction to the arrows on the diagram.

So this vector is negative a, subtract b.

Or negative b, subtract a.

B to D is positive b, negative a.

So we write this as b subtract a.

D to B is negative b add a.

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.

Congruent means the same size.

So, all four of these parallelograms are identical.

This means that the length AC is 2a, because it is double the length AB.

The length DC is a subtract b.

The length DI is 2a add b.

Shape A, B, C, D is a trapezium.

We're going to write the vector AC in terms of a and b.

For this vector, we're going to start at A, travel to B and then to C.

This is 4a, add a, add b, which simplifies to 5a, add b.

Next, we're going to write the vector for AD.

This isn't a add b as it is not parallel, or the same length as BC.

We're starting at the point A, then to B, then moving to C and finally to D.

We know that A to C is 4a, add a, add b we're then adding on CD.

We need to work out the length CD.

We are told that DC is equal to 1.

5AB.

We're going to multiply the length 4a by 1.

5.

This gives us 6a.

C to D is negative 6a.

This expression simplifies to b subtract a.

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 length CA is 5a add 3b.

And the length AD is negative 2a subtract 3b.

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 length DC is 8a, as it is double AB.

The length BD is written as negative 5a subtract b.

And the length CB is written as negative 3a add b or b subtract 3a.

That's all for this lesson.

Thanks for watching.