Lesson video

Hi, I'm Miss Davies and in this lesson, we're going to be adding together two or more column vectors.

When we are adding two column vectors together, think about it like this.

This example, the horizontal components, are two to the right, and then a further four to the right.

This means that this vector in total is six units to the right.

The vertical components, we've got three squares up, and then a further five squares up.

Three is gone.

Eight squares up in total.

The resultant vector is six, eight.

With this next example, the horizontal components, you've got four squares to the right, and then two squares to the left.

Overall, this is two squares to the right.

This four, add negative two is positive two.

The vertical components, we've gone three units down, and then three units up.

This means that it hasn't moved at all in a vertical direction.

Negative three add three is zero.

The resultant vector is two, zero.

Here's some questions for you to try.

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

Here we got this, simply add together the horizontal components and then add together the vertical components to get the resultant vector.

Here are some questions for you to try.

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

To answer these questions, you need to substitute the correct column vectors into each of the expressions and then add the horizontal components and then add the vertical components.

From this diagram, we can see that vector A can be written as three, four, as it is three squares to the right and four up.

vector B can be written as two, negative one, as it is two squares to the right and one down.

This means that A plus B can be written as three, four up to, negative one.

To travel from the start of vector A to the end of vector B, we move five squares to the right, and three squares up.

This is the same as three add two to get five, and four add negative one to get three.

The resultant vector of A plus B, is five, three.

Here is some questions for you to try.

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

Here are the answers.

Vector X, is the column vector four, four and vector Y can be written as three, negative two.

Check that you got these right.

Here is some questions for you to try.

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

Here are the answers.

Vector A can be written as three, three, vector B as four, negative one and C as zero, three as this doesn't have a horizontal component as it only goes up.

That's all for this lesson.

Thanks for watching.