Vectors can be written and added using different notations such as arrows or underlining. The length of a vector is represented by its modulus. Pythagoras' theorem can be used to find the length of the hypotenuse of a right-angled triangle if the other two sides are known. Vectors can be broken down into their horizontal and vertical components using trigonometry, and combined to find the resultant vector.

1. Chapter 8 – Mapping Space and Time 8.2b – Maps and Vectors We will find out: How vectors should be written How resultant vectors can be calculated

2. What do Vectors tell us? We know from last lesson that: There is more than one way to get to a destination a b c In this case, a + b = c – THEY ARE THE EQUIVALENT JOURNEY!!! For vectors we are only interested in the end result, not how we get there. This is also known as the resultant . Vectors add by placing them ‘tip to tail’

3. Writing Vectors Vectors are written like this a – bold type or this a – a line underneath or this a – an arrow on top These are the NOTATIONS to indicate that a value is a vector and not just a number! To indicate the magnitude of a vector, the modulus sign | | is used. ie. | a | or | a | or | a |

4. Pythagoras’ Theorem For a right-angles triangle a 2 + b 2 = c 2 a b c or hypotenuse

5. Find the length of the hypotenuse

6. Answers 1. 10.296 cm (3 d pl) 2. 3.225 cm (3 d pl) 3. 15.264 cm (3 d pl) 4. 102.005 cm (3 d pl)

7. 5. In a triangle abc, angle a = 90 degrees, ab = 11.3 cm, bc = 15.2 cm. Find ac. 6. In a triangle abc, angle a = 90 degrees, ab = 14 cm, bc = 15 cm. Find ac. 7. In a triangle abc, angle a = 90 degrees, ab = 0.03 cm, bc = 0.05 cm. Find ac. 8. Miss this one out! 9. A ship sails 32 nautical miles due north then sails 22 nautical miles due east. How far is it from its starting point ? 10. The diagonal AC of a rectangle ABCD is 0.67 m long and side Ab is 0.32 m long. How long is side BC ? Draw these and try them!

8. More Answers 5. 10.166 cm (3 d pl) 6. 5.385 cm (3 d pl) 7. 0.04 cm (2 d pl) 8. n/a 9. 38.833 nautical miles (3 d pl) 10. 0.5886 m (3 d pl)

9. Other Calculations We can calculate the components of a vector using trigonometry.

11. Trigonometry – Finding Angles Complete Exercises on worksheet http://www.funmaths.com/worksheets/downloads/view.htm?ws0036_1.gif

13. Relative Velocity Do objects always go where you think that they will? http://www.metacafe.com/watch/39256/crosswinds/