practice_midterm1.pdf - Midterm Exam 1 Sample Math 32A/3...

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Midterm Exam 1 — Sample Math 32A/3, Fall 2014 This is a collection of problems that would not be unreasonable for a real midterm exam. WARNING: the inclusion (or exclusion) of a certain topic or type of problem on this sample exam does not guarantee its inclusion (or exclusion) on the actual exam! 1. (a) Parametrize (in vector form) the line tangent to r ( t ) = h e t/π , sin t, t i at t 0 = π . (b) Find a normal vector for the plane containing the point P = ( - 1 , 0 , 1) and the line parametrized by r ( t ) = h t + 1 , 2 t, - 1 i .
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2. (a) Consider the plane curve with parametrization r ( t ) = h 3 t 2 , 1 1+ t i for t > - 1. Find the length of v = R 1 0 r ( t ) dt . (b) Let u and v be perpendicular unit vectors in R 3 . In terms of u and/or v , describe the vector u × ( u × v ). Justify your answer!
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3. The following vectors span a parallelepiped
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