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Unformatted text preview: MATH 210 Selfquiz 3 February 01, 2009 1. Consider the motion given by the vector valued function r ( t ) = < 3 sin(2 t ) , 3 cos(2 t ) , t > . Find its velocity, its acceleration and its speed. Solution: The velocity is given by: v ( t ) = r ( t ) = < 6 cos(2 t ) , 6 < sin(2 t ) , 1 > The speed is given by: v ( t ) =  v ( t )  = q 6 2 cos 2 (2 t ) + 6 2 sin 2 (2 t ) + 1 = q 36(cos 2 (2 t ) + sin 2 (2 t )) + 1 = 37 The acceleration is given by: a ( t ) = v ( t ) = < 12 cos(2 t ) , 12 cos(2 t ) , > 2. Find the distance between the planes with equations x + 2 y z = 1 and x + 2 y z = 13. Solution: We first need to identify a vector which is simultaneously per pendicular to the two planes. By inspecting the equations, we see that such a vector is < 1 , 2 , 1 > . Our plan is to find a line which is perpendicular to both planes and compute the distance between the points at which the line meets the two planes....
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This note was uploaded on 10/27/2009 for the course ED 210 taught by Professor Thorkildeson during the Spring '09 term at Ill. Chicago.
 Spring '09
 Thorkildeson

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