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Acknowledgements

All materials included in this unit are derived from content originated at the Open University.


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1.5 Exercises

Exercise 1

A vector a has magnitude |a| = 7 and direction θ = −70°. Calculate the component form of a, giving the components correct to two decimal places.

<
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1.4.1 Bearings

In the following subsections, we apply the vector ideas introduced so far to displacements and velocities. The examples will feature directions referred to points of the compass, known as bearings.

The direction of Leeds relative to Bristol can be described as ‘15° to the East of due North’, or N 15° E. This is an instance of a bearing. Directions on the ground are typically given like this, in terms of the directions North (N), South (S), East (E)
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1.3: Summing vectors given in geometric form

The following activity illustrates how the conversion processes outlined in the preceding sections may come in useful. If two vectors are given in geometric form, and their sum is sought in the same form, one approach is to convert each of the vectors into component form, add their corresponding components, and then convert the sum back to geometric form.

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1.2: Converting to geometric form

You have seen how any vector given in geometric form, in terms of magnitude and direction, can be written in component form. You will now see how conversion in the opposite sense may be achieved, starting from component form. In other words, given a vector a = a 1 i + a 2 j, what are its magnitude |a| and direction θ?

The first part of this question is dealt with using Pythagoras’ Theorem: the magnitude of a v
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Learning outcomes

On completion of this unit you should be able to:

  • convert a vector from geometric form (in terms of magnitude and direction) to component form;

  • convert a vector from component form to geometric form;

  • understand the use of bearings to describe direction;

  • understand the difference between velocity and speed;

  • find resultant displacements and velocities in geometric form, via the use of components.


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Introduction

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as shown in Section 2, in which you will also work with bearings.

This unit is an adapted extract from the Open University course
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Acknowledgements

All materials included in this unit are derived from content originated at the Open University.


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References

Hart, K., Kerslake, D., Brown, M., Ruddock, G., Kuchemann, D. and McCartney, M. (eds) (1981) Children's Understanding of Mathematics 11-16, London, John Murray.
McCague, W. (2003) 'A mathematical look at a medieval cathedral', Math Horizons, April, pp.11-15 and p.31. See also http://www.maa.org.
Phill
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1.6.2 Alerts

Online bookshops and some of the major search engines offer ‘Alerts’ services. These work by allowing you to set up a profile once you have registered on their site, and when there are items meeting your criteria you receive an email. The good thing about alerts is that you don’t have to do anything once you have set up your profile. The downside, particularly with alerts services from the search engines, is that given the extent to which internet traffic is on the increase whether new
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1.6.1 Introduction

The process of keeping up-to-date in your chosen subject area is useful for your studies and afterwards, for your own personal satisfaction, or perhaps in your career as part of your continuing professional development.

There are a great many tools available that make it quite easy to keep yourself up to date. You can set them up so that the information comes to you, rather than you having to go out on the web looking for it. Over the next few pages, you will be experimenting with some
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1.5.7 Referencing

We mentioned above that we need to reference sources to ensure we abide by copyright legislation. But there is another reason we need to give accurate references to items we use – so we can share it.

Consider this scenario. A friend says they’ve just read an interesting article where Joshua Schachter, founder of del.icio.us has spoken about why it isn’t a faceted search system, and you should read it. How would you go about finding it? Would you start looking in a news database, a
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1.5.6 Copyright – what you need to know

An original piece of work, whether it is text, music, pictures, sound recordings, web pages, etc., is protected by copyright law and may often have an accompanying symbol (©) and/or legal statement. In the UK it is the Copyright, Designs and Patents Act 1988 which regulates this.

In most circumstances, works protected by copyright can be used in whole or in part only with the permission of the owner. In some cases this permission results in a fee.

However, the UK legislation incl
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1.5.4The 5 Ds

If you don’t use a system at all, then you could suffer from the effects of information overload:

  • losing important information

  • wasting time on trying to find things

  • ending up with piles of physical and virtual stuff everywhere

One technique you might like to apply to your files (be they paper or electronic) is the 5Ds. Try applying these and see if you can reduce your information overload.


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1.5.3 Desktop search tools

Finding your paperwork or electronic files can be a problem. You may find that even if you do have some sort of filing system, your structure soon gets quite large with files in multiple locations, which can be hard to navigate. You may find yourself making arbitrary decisions about which folder to place a document in. It may make sense now but in the future, when you look where you think it should be, it’s not there.

At times like this you may resort to the search command from the Wi
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1.5.1 Why is it important to be organised?

  • 87% of items that are filed into a filing cabinet are never looked at again. STANFORD UNIVERSITY

  • The world is producing nearly two exabytes of new and unique information every year – an exabyte is a new term that had to be coined for a billion gigabytes. All the words ever spoken by human beings comes to five exabytes. UNIVERSITY OF CALIFORNIA (BERKELEY)

  • More new information has been produc
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1.4.8 Summary

In this section we have introduced you to the PROMPT checklist as a useful tool for assessing the quality of any piece of information. If you use it regularly you will find that you develop the ability to scan information quickly and identify strengths and weaknesses. As a closing exercise you might like to pick one of the websites below or any of your own choice and try to evaluate it using the PROMPT criteria. To make it easier for you we have provided a printable checklist (see below).


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1.4.6 P is for Provenance

The provenance of a piece of information (i.e. who produced it? where did it come from?) may provide another useful clue to its reliability. It represents the 'credentials' of a piece of information that support its status and perceived value. It is therefore very important to be able to identify the author, sponsoring body or source of your information.

Why is this important?

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1.3.8 Choosing the right tool for the job

Before searching it is always a good idea to check what the source you have chosen covers to make sure it will unearth information that matches your search need (you will notice that all the resources we’ve covered in this guide have short descriptions to enable you to decide which to use). Some of the decision makers, depending on the context of your search might be:

  • Does it have full text?

  • Does it cover the right subject?


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1.3.2 Search engines and subject gateways

Although both search engines and subject gateways will help you find the resources that you need, the types of information that you find will differ.

Search engines such as Google and Yahoo! search the internet for keywords or phrases, and then show you the results. These results are not mediated by the search engines, and therefore you need to use your own judgement on the reliability of the results. You may, for example, find websites written by experts, alongside websites written by
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