Main Points: Some equations do not have solutions due to the number of equations being larger than the number of variables. For example, three equations with two variables will sometimes not have a solution. When this happens, an approximate solution is found. Dot products help to find approximate solutions to these equations.
Challenges: I understand the information about having to find approximate solutions, but I'm a little fuzzy as to where dot products come in to help.
Reflections: I still can't really comprehend why this is important in real life. The parts about angles and lenghts make sense, but when would you use something like this in the real world? Maybe more of what I'm asking is what kind of question/problem would lead you to use dot products to help find an approximate solution?
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