MAT2500-01/04 18S Quiz 3 Print Name (Last, First) _________________________________|__Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use EQUAL SIGNS and arrows when appropriate. Always SIMPLIFY expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC).Given the vector-valued function 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 , 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 (no credit for unidentified expressions in your responses):
a) Evaluate 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 and remember to simplify your results.
b) Evaluate 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, 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 and remember to simplify your results.
c) Evaluate the exact angle \316\270 in radians between 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 and 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 and a single decimal place approximation in degrees.
d) Evaluate the vector 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 which is the vector projection of 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 orthogonal (perpendicular!) to 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.solutionRemark: The second derivative is scaled down in order not to distort the 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We introduce the position vectors and the two relevant difference 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