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Vectors Assignment QUESTION 1 – 40 marks You work for Oz-Vector Airline and you have been asked to set accurate routings between airports around Australian cities. Your job is to design at least three routes between a minimum of three major cities, validating their accuracy using mathematics. You will be producing a vector map, with these routes, and all the relevant information about these routes. Your vector map must include: • Starting point and destination for each vector on an accurate scale • Each vector (shown as arrows) on the path • Scale and orientation shown correctly on your map Your calculations must include: • Calculated total distance to each location (scalar) • Calculated total displacement (vector) with its magnitude and direction. You will have the opportunity to discuss your drawings and calculations with your tutor before final submission during consultations. You may use google maps and other web pages to help you with this assignment, however, you must reference all the resources used in text, and you must list it in your reference page, as per any project or academic assignment. QUESTION 2 – 10 marks Besides adding vectors, we can also subtract vectors by two graphical techniques. Explain and demonstrate how subtraction can be done using these graphical techniques. You will need to produce a vector map, with your chosen vectors, and all the relevant information about the subtraction methods.
QUESTION 3 – 20 marks
The picture above shows a person pushing a sled and also pulling a sled at the same angle, friction is the same regardless of whether he is pushing or pulling the sled. Model this situation with different forces and angles of your choice, show all your working on your assignment. According to your calculations, since the angle is the same when he is pushing and when he is pulling, when will the sled move faster? That is, which of these will get them to their destination sooner?
QUESTION 4 – 30 marks (a) Explain in detail the different ways to multiply two vectors, the names and the symbols used. Use your own examples, that is, make up three vectors and name them, for example a, b and c, to highlight how these operations are done. (b) Find one physical application where the cross product is used. Explain these application with your own examples (c) With two of your own examples from part (a) explain and show why the cross product between two vectors is anti-commutative.
Performance Objectives: Know: Represent a vector both algebraically and graphically Perform operations with vectors, along with algebraic and graphic representations Do: Analyze and describe the geometry of vectors Perform mathematical operations with vectors Use vectors to solve real-world problems Browse and search the Internet Create electronic documents using graphics Cite sources within documents appropriately