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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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    Forces, velocities, small displacements are some of the main physical examples.2012-06-26

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You might like to take a look at an article by J. Kolecki from NASA: "An Introduction to Tensors for Students of Physics and Engineering". 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.