Lesson Vectors
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• Slide 1
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Vectors

A review of what you need to know about vectors for IGCSE • Slide 2
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Summary

• A vector has both magnitude and direction

• Vectors can describe translations

• Vectors can be added, subtracted and multiplied by a scalar (fancy maths word for a number)

• Position vectors always start from the origin

• There's lots more to know about vectors but not for IGCSE

• Slide 3
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How to represent a vector

1. Column vector
2. Line with an arrow • Question 4
60 seconds
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Write vector A as a column vector. Click on the correct answer below.   • Question 5
45 seconds
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Vector B can be written as a column vector where the top number is m and the bottom number is n. What is the value of n?

-2

1

1.5

-3

• Question 6
45 seconds
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Vector B can be written as a column vector where the top number is m and the bottom number is n. What is the value of m?

-2

1

1.5

-3

• Slide 7
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Magnitude of a vector

To find the magnitude of a vector we use Pythagoras theorem. Don't forget the notation! • Question 8
120 seconds
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The magnitude of this vector is

$\sqrt{k}$   what is the value of k?

10
• Question 9
300 seconds
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Q.

A vector goes from the point (-2,7) to the point (4,5) it's magnitude is

$\sqrt{m}$  what is the value of m?

40
• Question 10
120 seconds
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13
• Slide 11
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Vectors to describe translations.

Triangle C is translated by vector a to give triangle C'.  Where will the new triangle be? What are the coordinates of P' (where point P ends up)? • Slide 12
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Where was triangle C'?

If you answered that the coordinates of P' were (0,2) then you are correct! This translation moves the triangle 4 to the right and down 1. • Slide 13
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What is the distance between triangle C and triangle C'?

Did you realise that the distance between the 2 triangles is the magnitude of vector a (remember we write that|a|)?

So the answer here is square root of 17. • Slide 14
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Multiplying a vector by a scalar.

(A scalar is just a fancy word for number) • Slide 15
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Multiplying a vector by a negative number.

Text • Slide 16
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Multiplying a vector by a fractional scalar.

Text • Slide 17
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Text • Question 18
120 seconds
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Enter the numbers a,b - you need to type in the 2 numbers separated by a comma with no space.

6,14
• Slide 19
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Draw the first vector and where it finishes start drawing the second vector. • Slide 20
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How to subtract column vectors.

Text • Slide 21
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Subtracting vectors graphically

As for addition draw the first vector and then at the end of it draw the second vector but going in the opposite direction. • Slide 22
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Position Vector

The position vector is the vector from the origin to a point. • Slide 23
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Now lets try a few IGCSE questions

Text
• Question 24
120 seconds
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-4
• Question 25
120 seconds
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x+7y
• Slide 26
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Try this question on paper. Then check your answers on the next slide.

Text • Slide 27
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Title

Here are the answers. On the next slide you can see a video explanation of how I got them. • Slide 28
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Explanation of the last question.

Text
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