math 265

# math 265 - plane 3 Show that the parametric curve x t,y t,z...

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Math 265 (Butler) Practice Midterm I – A Try to answer the following questions without the use of book, notes or calculator. Time yourself and try to ﬁnish the test in less than 50 minutes. 1. A particle moves through three dimensional space with velocity v ( t ) = h sec 2 t, 2 sec t tan t, tan 2 t i . At time t = 0 the particle is at h 0 , 1 , 2 i , ﬁnd the position function of the particle for - π/ 4 t π/ 4. 2. Find the points on the plane x +2 y = 5+3 z which is closest to the point (4 , 4 , - 7). (Hint: you do not need calculus to ﬁnd the answer. Useful hint: the line that connects the point (4 , 4 , - 7) to the nearest point on the plane will be perpendicular to the
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Unformatted text preview: plane.) 3. Show that the parametric curve ( x ( t ) ,y ( t ) ,z ( t )) = (1-sin(2 t ) , √ 2(sin t + cos t ) , cos(2 t )) lies on a sphere centered at the origin. Also, ﬁnd the radius of the sphere. 4. Find the area of the quadrilateral in the plane with vertices located at (3,1), (7,3), (4,4) and (0,3) using vector techniques. 5. Find the cumulative length function s ( t ) (starting from a = 1) of the parametric curve h ln t, 2 t, 1 2 t 2 i ....
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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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