2313f10-practice-final - NAME MAC 2313 Fall 2010 Practice...

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NAME : MAC 2313 — Fall 2010 Practice Final Please Note: We will discuss this exam on Tuesday 11/7 and Wednesday 11/8. I apologize in advance that I won’t be able to post solutions. If you want to find out the solutions, you should come to class on Tuesday and Wednesday. The actual final exam will have a di ff erent format than this exam. The actual final exam will be shorter than this exam. The actual final exam will provide the double angle identities for sin and cos.
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1. (10) For each of the following, answer MEANINGLESS, SCALAR, or VECTOR (or M, S, V) if the given expression is nonsense, is sensible and gives a scalar answer, or is sensible and gives a vector answer, respectively. In all of them, a , b , and c are vectors with numerical components, F is a vector field, and f is a scalar function. i. a · ( b × c ) ii. a × ( b · c ) iii. a · ( b · c ) iv. a × ( b × c ) v. ∇ × f vi. ( · f ) vii. · ( f ) viii. ∇ × ( f ) ix. ( · F ) x. · a xi. ∇ × a xii. a · F Which of the meaningful expressions above always evaluate to 0 or 0 ?
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