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    Vector calculations

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    Show that (a x b)â?¢(c x d)=(a â?¢ c)(b â?¢ d)-(a â?¢ d)(b â?¢ c). Suppose that A, B, C are three points equidistant from O and that the segments BC, CA, AB subtend angles x, y, z respectively at O. Show that cosx=cosycosz+ sinysinzcosw, where w is the angle between the planes AOB and AOC.

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    Solution Summary

    This solution thoroughly demonstrates vector calculations.