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2. Translation Sliding vector Horizontal Steps Vertical Steps = O I

3. © T Madas Translation Sliding vector Horizontal Steps Vertical Steps = O I A vector: is a line with a start and a finish. A vector has a direction and a length.

4. © T Madas Translation Sliding vector Horizontal Steps Vertical Steps = Component A vector: is a line with a start and a finish. A vector has a direction and a length.

5. © T Madas Translation Sliding vector Horizontal Steps Vertical Steps = Component If a vector is drawn on a grid we can always write it, in component form.

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7. A vector is a line with a start and a finish. It therefore has: 1.line of action 2.a direction 3.a given size (magnitude) A B A B

8. © T Madas we write vectors in the following ways: By writing the starting point and the finishing point in capitals with an arrow over them With a lower case letter which: is printed in bold or underlined when handwritten In component form, if the vector is drawn on a grid: 4 5

9. © T Madas E F A B C D G H

10. 4 5 A B -5 4 C D AB = CD =

11. © T Madas 4 5 4 0 0 5 4040 0505 + = 4 5 A B AB =

12. © T Madas -5 4 0 0 4 0 0404 + = -5 4 C D CD =

13. © T Madas What is the vector from A to B ? What is the vector from B to C ? What is the vector from A to C ? A B C 5 2 3 4 8 6 5252 3434 + = 8 6 AB = BC = AC = AB+ BC = AC

14. © T Madas A B C 5252 3434 8686 5252 3434 + = 8686 AB = BC = AC = AB+ BC = AC To add vectors when written in component form: we add the horizontal components and the vertical components of the vectors separately.

15. © T Madas 3232 Let the vector u = 3232 3232 2 x = u = u2 x2 x What is the vector 2u ? 6 4 2u = 2 x 3 2 x 2 = 6464 To multiply a vector in component form by a number (scalar), we multiply each vector component by that number.

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17. + Let the vectors u =, v = and w = 5353 7171 -4 2 Calculate: 1. u + v u v 5353 = 7171 12 4 u + v

18. © T Madas + Let the vectors u =, v = and w = 5353 7171 -4 2 Calculate: 2. u + v + w u v 5353 = 7171 8 6 u + v + w + -4 2 w

19. © T Madas + 2 Let the vectors u =, v = and w = 5353 7171 -4 2 Calculate: 3. u + 2w u 5353 = -3 7 u + 2w -4 2 2w2w + 5353 -8 4 =

20. © T Madas – Let the vectors u =, v = and w = 5353 7171 -4 2 Calculate: 4. u – v u 5353 = -2 2 u – v 7171 -v-v + 5353 -7 = v

21. © T Madas – Let the vectors u =, v = and w = 5353 7171 -4 2 Calculate: 5. u – w u 5353 = 9 1 u – w -4 2 -w-w + 5353 4 -2 = w

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23. What is the magnitude of vector r = ? xyxy x y d xyxy r = d 2d 2 =x 2x 2 +y 2y 2 c d=x 2x 2 +y 2y 2 r=x 2x 2 +y 2y 2

24. © T Madas ( ) 2 -5 12 What is the magnitude of vector r = ? xyxy r=x 2x 2 +y 2y 2 a = 8686 a=8282 +6262 =64+36=100= 10 units b = b=+12 2 =25+ 144 =169= 13 units ( ) 2 -6 -2 u = u=+(-2) 2 =36+ 4 =40≈ 6.3 units v = 7 24 v=7272 +24 2 =49+576=625= 25 units

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26. An object is translated using the vector followed by a second translation by the vector. Work out the vector for the combined translation. 7373 -5 4 + 7373 = -5 4 2 7 7373 -5 4 2727

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28. 5252 = 5 12 + 5757 + -6 An object is placed at the origin of a standard set of axes and is subject to four successive translations using the following vectors:,, and. 1. Work out the single vector that could be used to produce the same result as these four translations. 2. Calculate the magnitude of this vector. 7878 3 -6 5757 + 7878 3 magnitude=+12 2 =25+ 144 =169= 13 units

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30. The points O (0,0), A (1,5) and B (-1,2) are given. 1. Write AB as a column vector and calculate its magnitude. The point C is such so that: AC is parallel to AB = BC 2. Write AC as a column vector. The point D is such so that: ABCD is a rhombus 3. Calculate the area of the rhombus. 0 x y O A B -2 -3 AB = ( ) 2 -2 -3 AB = AB=+ (-3) 2 =4+ 9 = 13 ≈ 3.6 units

31. © T Madas The point C is such so that: AC is parallel to AB = BC 2. Write AC as a column vector. The point D is such so that: ABCD is a rhombus 3. Calculate the area of the rhombus. 0 The points O (0,0), A (1,5) and B (-1,2) are given. 1. Write AB as a column vector and calculate its magnitude. x y O A B 0 C 0 -6 AC =

32. © T Madas The point C is such so that: AC is parallel to AB = BC 2. Write AC as a column vector. The point D is such so that: ABCD is a rhombus 3. Calculate the area of the rhombus. 0 The points O (0,0), A (1,5) and B (-1,2) are given. 1. Write AB as a column vector and calculate its magnitude. x y O A B C D 3 3 3 3 12

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