pm1bSolns - Math 265 (Butler) Practice Midterm I B...

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Unformatted text preview: Math 265 (Butler) Practice Midterm I B (Solutions) 1. Find the projection of h 2 s, 1 ,s- 1 i onto the vector h- 2 t, 5- t 2 , 4 t i . The formula for projection of a vector u onto a vector v is u v v v v . Applying it to our case with u = h 2 s, 1 ,s- 1 i and v = h- 2 t, 5- t 2 , 4 t i we have that the projection is h 2 s, 1 ,s- 1 i h- 2 t, 5- t 2 , 4 t i h- 2 t, 5- t 2 , 4 t i h- 2 t, 5- t 2 , 4 t i h- 2 t, 5- t 2 , 4 t i = (2 s )(- 2 t ) + (1)(5- t 2 ) + ( s- 1)(4 t ) (- 2 t ) 2 + (5- t 2 ) 2 + (4 t ) 2 h- 2 t, 5- t 2 , 4 t i =- 4 st + 5- t 2 + 4 st- 4 t 4 t 2 + 25- 10 t 2 + t 4 + 16 t 2 h- 2 t, 5- t 2 , 4 t i = 5- 4 t- t 2 t 4 + 10 t 2 + 25 h- 2 t, 5- t 2 , 4 t i = 5- 4 t- t 2 ( t 2 + 5) 2 h- 2 t, 5- t 2 , 4 t i . (On a side note we see that this projection only depends on t , even though the vector we were projecting involved s .) 2. A particle travels along the parametric curve h e- t cos t,e- t sin t i starts at (1 , 0) at time t = 0 and then spirals into the origin (0...
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This note was uploaded on 02/06/2012 for the course MATH 265 taught by Professor Gregorac during the Spring '08 term at Iowa State.

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pm1bSolns - Math 265 (Butler) Practice Midterm I B...

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