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What is a good way to introduce vectors on a linear algebra course so that students are motivated from the start? I need an opening which will have a real impact. Are there any motivating examples?

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There are lots of facts in classical Euclidean geometry that can be proven using vector methods; proving a couple of these should interest mathematically-inclined students. Also, the physical world provides no shortage of vectorial quantities that would appeal to the physics-minded e.g., the wind's velocity at a given point, tangential acceleration of a ball swinging about a pole, etc. –  ItsNotObvious Jun 26 '12 at 21:19
    
Forces, velocities, small displacements are some of the main physical examples. –  Michael Jun 26 '12 at 21:20
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You might like to take a look at an article on tensors by J. Kolecki from NASA: http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/documents/Tensors_TM2002211716.pdf. Although the article is primarily about tensors, he motivates them by motivating vectors in the introduction. He has a really nice way of explaining what scalars, vectors, and tensors are all about - all of my explanations to students are based off of his article.

Good luck.

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