Unformatted text preview: (b) Write down a piecewise parametrization of the curve shown below with clockwise orientation. [10 pts] The curved part is the parabola y = 4x 2 . Please put problem 4 on answer sheet 4 4. (a) Give the parametric equations of the line through (1 , 2 , 3) and perpendicular to both vectors [10 pts] 2ˆ ı + 2 ˆ + 0 ˆ k and 3ˆ ı1 ˆ + 2 ˆ k . (b) Find the point at which the line ¯ r ( t ) = (2 t + 2)ˆ ı + (5t ) ˆ + ( t + 10) ˆ k passes through the [10 pts] plane 2 x + yz = 1. Please put problem 5 on answer sheet 5 5. (a) Sketch the plane 2 x + y + 3 z = 12. Mark at least three points with their coordinates. [10 pts] (b) Set up (do not evaluate) the integral for the length of ¯ r ( t ) = t 2 ˆ ı + t 3 ˆ 1 ˆ k for 0 ≤ t ≤ 1. [10 pts]...
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 Spring '08
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 Math, Parametric equation

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