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Hi! I'm Miss Davies! In this lesson we're going to be finding the length of a column vector.

We're going to find the length of the vector six, eight.

If we draw this vector it is six squares to the right and eight up.

We can then use Pythagoras' theorem to find the length of the vector as this is a right angle triangle.

Six squared is 36 and eight squared is 64.

36, add 64, is 100.

The square root of 100 is 10.

So the length of this vector is 10 units.

If we're finding the length of the vector three, negative four, we're going to do three squared, add negative four squared.

Three squared is nine, negative four squared is positive 16.

These add up to make 25.

Square root of 25 is five.

So this vector is five units.

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 values within the column vectors are always going to be the shorter length of the right angle triangle.

Remember that a negative value squared always gives a positive result.

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 of the vector is the hypotenuse of the right angle triangle.

The vector r is four, negative two.

We have been asked to calculate the length of two r.

The vector, two r, is eight, negative four.

This is calculated by multiplying both the horizontal and vertical components of the vector r by two.

We can apply Pythagoras' theorem to this vector to calculate the length of two r.

Eight squared, add negative four squared, is equal to two r squared.

The length of two r is 8.

94 units.

Here is a question for you to try.

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

Here is the answer.

To find the length of the vector three r multiply the components of vector r by three and then apply Pythagoras' theorem to find the length.

You could also have found the length of the vector r and multiplied this by three.

That's all for this lesson.

Thanks for watching!.