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Three Dimensional Geometry

Question

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If a line has direction ratios 2, -1, -2, determine its direction cosines.

Solution

Direction ratios of the line are 2, –1,–2.
Dividing each by

square root of left parenthesis 2 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared end root space equals space square root of 4 plus 1 plus 4 end root space equals space square root of 9 space equals space 3.

the direction cosines of line are

2 over 3 comma space minus 1 third comma space minus 2 over 3.

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