problem_set_2

# problem_set_2 - Name Section Last First MI Math 32A...

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1 Name: First MI Last Student ID # Problem Set #2 Score Section: C REDIT 2 1 0 Problem # 1 . Show that the points ( x , y , z ) which satisfy x 2 + y 2 + z 2 = 4 y – 2 z are a sphere by rewriting this equation in the “standard” form for a sphere. Identify explicitly the center and the radius of the sphere. C REDIT 2 1 0 Problem # 2 . Show that the points ( x , y , z ) which satisfy x 2 + y 2 + z 2 – 6 x + 4 y – 2 z = 11 are a sphere by rewriting this equation in the “standard” form for a sphere. Identify explicitly the center and the radius of the sphere. Math 32A Lecture #5 Fall 2007

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2 Problem Set #2 C REDIT 2 1 0 Problem # 3 . Show that the following three points in 3 D space: A = <–2,4,0> B = <1,2,–1> C = <–1,1,2> form the vertices of an equilateral triangle. C REDIT 2 1 0 Problem # 4 . Write, in the language of (2 D ) vectors the equation for the set of points r = <x,y> that form a circle of radius a and is centered at the point r 0 = < x 0 , y 0 >. Your final expression should involve only vectors, vector–style symbols and the scalar a .