Lesson video

Hi, I'm Miss Davies.

In this lesson we're going to be looking at vector diagrams that include ratios.

ABCD is a parallelogram.

D to Y to YC is in the ratio one to two.

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

As this is a parallelogram, the length DC is identical to AB, as it is the same length and it is parallel.

DY is 1/3 of DC, as we know that DY is 1/3 of this line and YC is 2/3 of this line.

This means that 2/3 of six a is two a.

The vector YC is 2/3 of DC, which is four 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 vector DX is equal to a and the vector AXE is equal to a subtract two b.

The shape ABCD is a trapezium.

A to X and X to D are in the ratio three to two.

We're going to write A to D in terms of a and b.

A to D is four a add a add b subtract six a.

This simplifies to b subtract a.

The vector AXE is 3/5 of AD.

This can be written as 3/5 multiplied by b subtract a.

DX is 2/5 of DA.

DA is a subtract b.

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 vector DX is 3/5 of DA.

This can be written as 6/5 a subtract 9/5 b.

The vector BX is 21/5 a subtract 6/5 b.

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 vector DM is 3/5 of DC.

DC is eight a, which means DM is 24 over five a.

DN is 1/2 DB, which means that DN is five over two a add 1/2 b.

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.

RS is eight a, which means RT is 14 a.

RU can be written as 11 a add four b.

That's all for this lesson.

Thanks for watching.