Lesson video

Hi, I'm Miss Davies.

In this lesson, we're going to be multiplying a column vector by a scalar.

Vector a is showed on our grid.

Vector a moves three unit to the right, and one unit down.

As a column vector, this can be written as three, negative one.

If we're going to draw the vector two a, it will look like this, as if a followed by another a.

As a column vector, this is six, negative two.

Both the horizontal and the vertical components of our column vector have been multiplied by two.

To write three a of a column vector, we're going to calculate three multiplied by three and three multiplied by negative one.

This gives us nine, negative three.

We can check this by drawing the vector three a.

We can see that it is nine units to the right and three units down.

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.

Both the horizontal and vertical components should have been multiplied by the same number.

Vector b is shown on the grid.

As a column vector, this can be written as five, negative two.

If we're drawing negative b, it has the same length, or magnitude, as vector b, it simply goes in the opposite direction.

As a column vector, negative b would be negative five, two, as it moves five units left and two units up.

Negative two b will be calculated by multiplying the column vector for b by negative two.

Negative two multiplied by five is negative 10, negative two multiplied by negative two is four.

We can check this by drawing two of vector b and unchanging the direction to give negative two b.

This moves 10 units to the left and four unit up.

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.

Negative b and b have the same length, but the directions are opposite to each other.

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.

Make sure you have multiplied both components of the vector by the same number.

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.

In question five, the vector a is four, three, the vector b is negative one, negative two, and vector c is negative five, one.

That's all for this lesson.

Thanks for watching.