JSFHMAT2500-01/04 12S 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 arrows and equal signs 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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 , (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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.solutiona) We introduce the position vectors and the two relevant difference 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a)QyktSSJyRzYiNiNJInRHRiUiIiItSSVldmFsRyUqcHJvdGVjdGVkRzYkLUklZGlmZkdGKzYkLUYkNiNJInhHRiVGMi9GMkYnRigtRio2JC1GLjYlRjBGMkYyRjNGKC1JKXNpbXBsaWZ5R0YlNiNJIiVHRiU=b)QyctSSJyRzYiNiMiIiJGJy1JJWV2YWxHJSpwcm90ZWN0ZWRHNiQtSSVkaWZmR0YqNiQtRiQ2I0kieEdGJUYxL0YxRidGJy1GKTYkLUYtNiVGL0YxRjFGMg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=a) again and b)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c)PkkmQWhhdDBHNiItSSIqRzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUdGJEkvVmVjdG9yQ2FsY3VsdXNHNiVGKEYoL0YqSShTdHVkZW50R0koX3N5c2xpYkdGJDYkLUklZXZhbEdGKDYkLUklZGlmZkdGKDYlLUkickdGJDYjSSJ4R0YkRjpGOi9GOiIiIiokLUklc3FydEc2JEYoRi82Iy1JMGRlbGF5RG90UHJvZHVjdEc2JEYoL0YqSSxUeXBlc2V0dGluZ0dGQDYkRjFGMSEiIg==QyktSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJJkFoYXQwR0YpSSNUMEdGKSIiIi1JJ2FyY2Nvc0dGKTYjSSIlR0YpRjAtSSZldmFsZkdGJjYjLUkiKkc2JEYmL0YoSS9WZWN0b3JDYWxjdWx1c0c2JUYmRiYvRihJKFN0dWRlbnRHRiw2JC1GOTYkRjQiJCE9KiRJI1BpR0YmISIiRjAtRjk2JC1GNjYkRjQiIiRJKGRlZ3JlZXNHRik=d)QyctSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJI1QwR0YpLUklZXZhbEdGJjYkLUklZGlmZkdGJjYlLUkickdGKTYjSSJ4R0YpRjhGOC9GOCIiIkY6PkkmQTBwYXJHRiktSSIqRzYkRiYvRihJL1ZlY3RvckNhbGN1bHVzRzYlRiZGJi9GKEkoU3R1ZGVudEdGLDYkSSIlR0YpRi5GOj5JJ0EwcGVycEdGKS1JIitHRj82JEYvLUkiLUdGPzYjRkY=Check:Ly1JJWV2YWxHJSpwcm90ZWN0ZWRHNiQtSSVkaWZmR0YlNiUtSSJyRzYiNiNJInhHRixGLkYuL0YuIiIiLUkiK0c2JEYlL0krbW9kdWxlbmFtZUdGLEkvVmVjdG9yQ2FsY3VsdXNHNiVGJUYlL0Y1SShTdHVkZW50R0koX3N5c2xpYkdGLDYkSSZBMHBhckdGLEknQTBwZXJwR0Yse) Here is the 3d plot:QyQtSSV3aXRoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJnBsb3RzR0YlISIiQyU+SSljdXJ2ZXBsdEc2Ii1JK3NwYWNlY3VydmVHRiU2Ji1JInJHRiU2I0kidEdGJS9GLDsiIiEkIiREIiEiIy9JKnRoaWNrbmVzc0dGJSIiJS9JJmNvbG9yR0YlSSZncmVlbkdGJSEiIi1JKGRpc3BsYXlHRiU2JEkiJUdGJS9JJWF4ZXNHRiVJJmJveGVkR0YlWe scale down the normal a bit so it does not distort the picture: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By rotating the picture so that the cyan vector is directly into the screen (a normal to the velocity-acceleration plane), we look perpendicular to the plane of the first (red = velocity) and second (blue = acceleration) derivative vectors, i.e., the acceleration plane, where we see the black vector (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNidRIndGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHRjQvJSxtYXRodmFyaWFudEdRLGJvbGQtaXRhbGljRicvJStmb250d2VpZ2h0R1ElYm9sZEYnLUkjbW9HRiQ2LlEuJlJpZ2h0VmVjdG9yO0YnLyUscGxhY2Vob2xkZXJHRjQvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZ1bnNldEYnLyUqc2VwYXJhdG9yR0ZHLyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRkcvJShsYXJnZW9wR0ZHLyUubW92YWJsZWxpbWl0c0dGRy8lJ2FjY2VudEdGRy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlYvRlNGNC1GLzYjUSFGJ0ZD) is the orthogonal projection of the acceleration vector perpendicular to the first derivative.
However, the units for the vectors are wrong for the scale of the original curve segment, which almost disappears in comparison, so we should scale them all back by a factor of 10 to see how they fit on the curve.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Here is an animation of the curve with the triad of unit vectors (set the number of frames to 11):LSYmSShTdHVkZW50R0koX3N5c2xpYkc2IjYjSS9WZWN0b3JDYWxjdWx1c0c2JCUqcHJvdGVjdGVkR0YmNiNJMFNwYWNlQ3VydmVUdXRvckdGJzYkLUkickdGJzYjSSJ0R0YnL0YyOyIiIS1JIipHNiRGKy9JK21vZHVsZW5hbWVHRidJL1ZlY3RvckNhbGN1bHVzRzYlRitGKy9GOkYlNiQiIiQjIiIiIiIjThe side and hypotenuse lengths of the projection triangle of the resolution of the acceleration with respect to the unit tangent are:LUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiM3Jy1JIipHNiRGJC9JK21vZHVsZW5hbWVHNiJJL1ZlY3RvckNhbGN1bHVzRzYlRiRGJC9GK0koU3R1ZGVudEdJKF9zeXNsaWJHRiw2JCIiIy1JJXNxcnRHNiRGJEYxNiNGM0YnLUYoNiQiIiQtRjU2I0Y6LUY1NiMiI05GPQ==Ly1JIitHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSS9WZWN0b3JDYWxjdWx1c0c2JUYmRiYvRihJKFN0dWRlbnRHSShfc3lzbGliR0YpNiQqJC1JIipHRiU2JCIiIy1JJXNxcnRHNiRGJkYuNiNGNEY0KiQtRjI2JCIiJC1GNjYjRjxGNCokLUY2NiMiI05GNA==This gives us a picture of the relative sizes of the three vectors: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TTdSMApJNlJUQUJMRV9TQVZFLzUxMTc3MjQwOFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkLCQqJCUidEciIiMjIiIiRiwsJCokRisiIiUjRi5GMSwkKiRGKyIiJyNGLkY1RiU=TTdSMApJNlJUQUJMRV9TQVZFLzUxMTc3NDY4OFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkLCQqJCUidEciIiMjIiIiRiwsJCokRisiIiUjRi5GMSwkKiRGKyIiJyNGLkY1RiU=TTdSMApJNlJUQUJMRV9TQVZFLzUxMTc3NTA0OFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkJSJ0RyokRikiIiQqJEYpIiImRiU=TTdSMApJNlJUQUJMRV9TQVZFLzUxMTc3NTQwOFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIiIiLCQqJCUidEciIiMiIiQsJCokRiwiIiUiIiZGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzUxMTc3NTUyOFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIiIiLCQqJCUidEciIiMiIiQsJCokRiwiIiUiIiZGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzUxMTc3NTg4OFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIyIiIiIiIyNGKiIiJSNGKiIiJ0YlTTdSMApJNlJUQUJMRV9TQVZFLzUxMTc3NjI0OFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIiIiRilGKUYlTTdSMApJNlJUQUJMRV9TQVZFLzUxMTc3NjYwOFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIiIiIiIkIiImRiU=TTdSMApJNlJUQUJMRV9TQVZFLzUxMTc0MTI5NlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkKiQsKCIiIkYrKiQlInRHIiIlRisqJEYtIiIpRisjISIiIiIjKiZGLUYzRipGMSomRi1GLkYqRjFGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzUxMTc0MjczNlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkLCQqJCIiJCMiIiIiIiMjRi1GK0YpRilGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzUxMTc0NjQ1NlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkLCQqJCIjTiMiIiIiIiMjRi1GKywkRiojIiIkRissJEYqI0YtIiIoRiU=TTdSMApJNlJUQUJMRV9TQVZFLzUxMTc1MDY1NlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIiIkRilGKUYlTTdSMApJNlJUQUJMRV9TQVZFLzUxMTc1MTg1NlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkISIjIiIhIiIjRiU=TTdSMApJNlJUQUJMRV9TQVZFLzUxMTc1MjIxNlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIiIiIiIkIiImRiU=TTdSMApJNlJUQUJMRV9TQVZFLzUxMTc1MjgxNlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIiIiIiIkIiImRiU=TTdSMApJNlJUQUJMRV9TQVZFLzUwNjgyNTY1NlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIyIiIiIiIyEiIkYpRiU=