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How to do vectors on TI-83 Calculator?

What is the best way to do 2d vectors on the TI-83? Netsearch found using complex numbers and some tricks using lists. I need to add vectors, do dot products, cross products, magnitude, conversions between r-theta and ihat jhat (rectangular) formats, area of parallelogram. PS, no programs allowed, teacher provides "clean" calculators for tests.

Update:

We've been using the clever list applications I mentioned above from the Brown articles you link to. His technique works almost directly for adding and multiplying vectors. He uses the Sum function with the lists to get the dot product. It appears TI-83 does not support functions like the cross product. Brown, TI, and other sources have downloadable functions, but we can't use those. I was hoping to find more clever tricks like the Brown articles, but can't.

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