## Quick Reference

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 cos^{2}*α*+cos^{2}*β*+cos^{2}*γ*=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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