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Math 2210-1. Practice Test 1. Fall 2007.
Name: September 15, 2007
Problem 1: /
Problem 2: /
Problem 3: /
Problem 4: /
Problem 5: /
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Instructions: The exam is closed book, closed notes and calculators are not allowed. You are only allowed one A4-size sheet of paper with anything on it. You will have 50 minutes for this exam. The point value of each problem is written next to the problem - use your time wisely. Please show all work, unless instructed otherwise. Partial credit will be given only for work shown.
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Problem 1(40 points) Let ~u = 2~i โ ~j + 2~k and ~v = 5~i + ~j โ 3 ~k be two vectors.
(1) Draw a sketch of vector ~u in the xyz-coordinate system. (2) Find the cosine of the angle between ~u and ~v. (3) Find the area of the triangle which has two sides ~u and ~v.
Problem 3(30 points) Consider the position vector
~r(t) = (cos t + sin t)~i + (sin t โ cos t)~j. (1) Find the acceleration ~a(t). (2) Find the normal and tangential components of the acceleration aN and aT. (3) What curve does ~r(t) describe?
Problem 4(30 points)
(1) Find the parametric equations of the line containing the point P (0, 1 , 2) and parallel to the planes 2x โ y + 3z = 5 and โx + 2 y + 2z = 3. (2) Is this line parallel also to the plane x + 3y โ z = 2?
