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ex2_fall11_2313

# ex2_fall11_2313 - Name MAC 2313 Exam 2 Version A SHOW ALL...

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Name: MAC 2313 Exam 2 Version A 09/21/2011 SHOW ALL YOUR WORK. Answers without procedure will be graded zero. [5]1. Find an equation for the plane that contains the lines x - 6 - 6 = y - 1 2 = z - 3 and x - 4 2 = y - 3 = z + 1 [4] 2. Reduce the equation to one of the standard forms, classify and sketch the surface, plot key point(s). 4 x 2 - y 2 + z 2 - 8 x - 2 y + 3 = 0 For problems 3, 4 and 5, consider the curve C with vector equation r ( t ) = h 3 sin t, 4 t, 3 cos t i , and the point P (0 , 0 , 3) on C [4] 3. Find parametric equations of the tangent line of C at P .

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[3] 4. If a particle travels along C , and starts at point P , find its position after 4 units of length. [3] 5. Find relationships between the components x ( t ), y ( t ) and z ( t ) and sketch the curve C . [3] 6. Write parametric equations for the curve of intersection between the paraboloid z = 4 x 2 + y 2 and the parabolic cylinder y = x 2 2
[5] 7. Find the curvature of r ( t ) = h t, t, 1 + t 2 i 8. A certain curve C that goes through the point P (1 , 0 , 0) when t = 0 has T ( t ) = h- sin t cos t, cos 2 t, - sin t i , and T 0 ( t ) = h sin 2 t - cos 2 t, - 2 sin t cos t, -

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