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direction ratios


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Suppose that a direction has direction cosines cos α, cos β, cos γ. Any triple of numbers l, m, n, not all zero, such that l=k cos α, m=k cos β, n=k cos γ, are called direction ratios of the given direction. Since cos2α+cos2β+cos2γ=1, it follows thatwhere either the+sign or the−sign is taken throughout. So any triple of numbers, not all zero, determine two possible sets of direction cosines, corresponding to opposite directions. The triple l, m, n are said to be direction ratios of a straight line when they are direction ratios of either direction of the line.

Subjects: Mathematics.


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