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hw3 - ∈ R n be the vertices of a regular tetrahedron i.e...

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MATH 427LAP HOMEWORK 3 Due Wednesday, Sept. 8 at 3:00PM Marsden and Tromba, 1.3 13,15ab,16c,18,22,14,27,36; 1.4 2,3,10,12,15; 1.5 2,7,8,9,13,16 Additional Problems: 1. Give parameterizations of the following surfaces. Be sure to state the constraints on your parameters! 1a. The portion of a sphere of radius 1, centered at the origin, for which x ≥ - 3 5 . 1b. The portion of a sphere of radius 1, centered at the origin, for which x ≥ - 3 5 and z ≥ - 3 5 . 2. Let p 1 , p 2 , p 3 , p 4
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Unformatted text preview: ∈ R n be the vertices of a regular tetrahedron, i.e., the distances || p i-p j || for i 6 = j are all equal. Let q be the center of mass of the face with vertices p 1 ,p 2 ,p 3 . Compute the cosine of the angle at p 4 made by the vectors q-p 4 and p 1-p 4 . [Hint: the answer does not depend on the coordinates of p 1 , ..., p 4 , as long as the distances between any two of them are the same. Pick nice coordinates!] 1...
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