10.3#12

Professor Taylor,

I've completed all of assignment 10.3, except for #12, which I don't know how to solve. Do you have any advise that might help me understand the problem?

The question is:

Assume that u⋅v=7, ∥u∥=4, and ∥v∥=3.
What is the value of 7u⋅(2u−2v)?

Thanks for the help.
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OK,  one critical piece of information that you might have missed is that we usually write |u| instead of ∥u∥ for vectors u, but both of these mean the same thing: the magnitude of the vector. Then you just need to know basic facts about the dot produce like ∥u∥^2=u.u  and the distributive law.