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Unformatted text preview: + cos 2 + cos 2 = 1 (1.18) was implicit in the work of the eighteenthcentury mathematicians Joseph Louis Lagrange (17361813) and Gaspard Monge (17461818), and explicitly stated by Leonard Euler (17071783) [ 4 , pp. 2067]. Using vector ideas, it is almost obvious. Proof of Equation ( 1.18 ) . Let u be a unit vector in the direction of the line. Then the angles between u and the unit vectors along the three axes are u = cos u = cos u k = cos from which it follows that u = cos + cos + cos k or in other words u = (cos , cos , cos ) ....
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 Fall '08
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 Calculus, Vectors, Dot Product

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