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Quandaries & Queries
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 Topic: cross product
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 An octagonal bird house 2007-01-13 From Soren:I'm in the process of building a birdhouse that is an octagon (based on previous questions, looks like that's a familiar tune). The essential elements are known, but I get stuck when trying to determine the angle for the cuts that would be made to the thickness of the wood so that they all fit together when assembled. Each octagonal section is 7 inches in width and the peak of the roof will be 2 inches higher than the sides. My sense is that the angle cuts that need to be made to the 'height' of each piece of wood. By height I mean the thinnest part of the wood that is neither the length nor the width to use colloquial terms. While it's clear that a slight angle is needed, it would seem that the angle would necessarily change as the distance from the top of any one side to the peak changes. Please advise if more clarification is needed. The 2 inches is random and can be changed if more convenient. Whew!Answered by Harley Weston. Vectors 2004-07-06 From Annie:a=3i-j+2k and b=i+3j-2k, determine the magnitude and direction cosines of the product vector and show that it is perpendicular to a vector c=9i+2j+2k.Answered by Chris Fisher. Multiplying vectors 2001-10-22 From Murray:Could you please explain why a vector times a vector is a scalar and how to derive the formula vector a * vector b = ab cos(a,b)Answered by Harley Weston.

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