MAT2500-01/04 17S 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZFLUYjNiZGKy1JJm1vdmVyR0YkNiUtSSNtaUdGJDYoUSJyRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0ZTRi8vRjNRLGJvbGQtaXRhbGljRicvJStmb250d2VpZ2h0R1ElYm9sZEYnLUYsNi9RLSZSaWdodEFycm93O0YnRi8vJSxwbGFjZWhvbGRlckdGU0YyL0Y2USZ1bnNldEYnL0Y4RltvL0Y6RlMvRjxGW28vRj5GW28vRkBGW28vRkJGW28vRkRRJjAuMGVtRicvRkdGY28vRkJGU0YvRjItRiw2LlEiJ0YnRi9GMkY1RjdGOUY7Rj1GP0ZBL0ZEUSwwLjExMTExMTFlbUYnRmRvLUkobWZlbmNlZEdGJDYlLUYjNiYtSSZtZnJhY0dGJDYoLUZONiZRJSZwaTtGJy9GVUYxRi9GMi1GIzYlLUkjbW5HRiQ2JVEiM0YnRi9GMkYvRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmJxLyUpYmV2ZWxsZWRHRjFGK0YvRjJGL0YyRitGL0Yy 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: This is a plane curve confined to the plane LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJ6RidGL0YyLyUrZXhlY3V0YWJsZUdGPUY5 which reduces the amound of work, since everything has to reflect this symmetry.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) We introduce the position vectors and the two relevant difference 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QyUtSStzcGFjZWN1cnZlRzYiNiUtSSJyR0YlNiNJInRHRiUvRio7IiIhLUkiKkc2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHRiVJL1ZlY3RvckNhbGN1bHVzRzYlRjEvRjNJKFN0dWRlbnRHNiRGMUkoX3N5c2xpYkdGJUYxNiQiIiNJI1BpR0YxL0kmY29sb3JHRiVJJHJlZEdGJSIiIi1JKGRpc3BsYXlHRiU2JkkiJUdGJS1JJmFycm93RzYkRjEvRjNJJnBsb3RzR0Y4NiUtRig2I0kkdGF1R0YlL0kmc2hhcGVHRiVGRi9GPkklYmx1ZUdGJS1GRjYmRkstSSVldmFsR0YxNiQtSSVkaWZmR0YxNiQtRig2I0kieEdGJUZmbi9GZm5GTUZOL0Y+SSZncmVlbkdGJS1GRjYmRkstRlU2JC1GWDYlRlpGZm5GZm5GZ25GTi9GPkklY3lhbkdGJQ==a)QyktSSJyRzYiNiNJInRHRiUiIiItSSVldmFsRyUqcHJvdGVjdGVkRzYkLUklZGlmZkdGKzYkLUYkNiNJInhHRiVGMi9GMkYnRigtRio2JC1GLjYlRjBGMkYyRjNGKC1JKXNpbXBsaWZ5R0YlNiNJIiVHRiU=QyUtSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiQtSSVldmFsR0YmNiQtSSVkaWZmR0YmNiQtSSJyR0YpNiNJInhHRilGNy9GN0kidEdGKUYuIiIiLUkiKkc2JEYmL0YoSS9WZWN0b3JDYWxjdWx1c0c2JUYmL0YoSShTdHVkZW50R0YrRiY2JEYuKiQtSSVzcXJ0R0YrNiNJIiVHRikhIiI=b)Qy8tSSJyRzYiNiNJJHRhdUdGJSIiIi1JJWV2YWxHJSpwcm90ZWN0ZWRHNiQtSSVkaWZmR0YrNiQtRiQ2I0kieEdGJUYyL0YyRidGKC1GKjYkLUYuNiVGMEYyRjJGM0YoLUkwZGVsYXlEb3RQcm9kdWN0RzYkRisvSSttb2R1bGVuYW1lR0YlSSxUeXBlc2V0dGluZ0c2JEYrSShfc3lzbGliR0YlNiRGKUYpRig+SSVUaGF0R0YlLUkiKkc2JEYrL0Y8SS9WZWN0b3JDYWxjdWx1c0c2JUYrL0Y8SShTdHVkZW50R0Y+Ris2JEYpKiQtSSVzcXJ0R0Y+NiNGOCEiIkYoLUY5NiRGNEY0RigtRkQ2JEY0KiQtRk42I0ZRRlA=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a) again and 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of the sides of the projection rectangle and its main 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