Math32a 1 R Kozhan Midterm 1 Oct 24 2011 Name UID Section TA Instructions If you get stuck move on to the next question You don t have a lot of time Make sure to look at the last question It s short and easy Free points Show all work if you want to get full credit I reserve the right to take off points if I cannot see how you arrived at your answer even if your final answer is correct No books notes electronics incl calculators and cell phones are allowed Good luck Question Max Your score 1 12 2 8 3 14 4 10 5 10 6 14 Total 68 1 Problem 1 a 4 points Find the center and the radius of the circle x2 y 2 4x 10y 0 b 8 points Find parametric equation for the path of a particle that moves around this circle twice counterclockwise starting from the top point of the circle 2 Problem 2 8 points Find the area of the triangle with vertices P 1 2 1 Q 2 3 0 R 1 0 1 3 Problem 3 a 4 points Find parametric and symmetric equations of the line through the point A 2 3 1 which is perpendicular to the plane 2y z 0 b 2 points Prove that this line is parallel to the line x 0 y 2 4t z 1 2t c 8 points Find the equation of the unique plane passing through both of the above lines 4 Problem 4 at time 10 points Find the unit tangent vector T and the principle normal vector N t t t t 2 of the curve r t he sin t e cos t e i 5 Problem 5 10 points Suppose r 00 t 2 j 6t k r 0 0 5 k r 0 2 i Find r 1 6 Problem 6 a 2 points Write the formula for the vector projection of a onto b b 2 points Let x t cos t y t sin t Find dy dx at t 4 Answer if the following statement is always TRUE or if it could be FALSE No justification is needed c 2 points Two lines in R3 perpendicular to a given line are parallel d 2 points Two planes in R3 perpendicular to a given line are parallel e 2 points Suppose a b c are nonzero vectors in R3 If a b a c then b c f 2 points Suppose a b c are nonzero vectors in R3 If a b a c then b c g 2 points Which one is true i If proj b a a then a b 0 ii If proj a b a then a b 0 7 Extra scratch paper 8
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