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Three Dimensional Geometry

Question

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

Solution

Direction ratios of the line are 1, – 3, 2.
Dividing each by

square root of left parenthesis 1 right parenthesis squared plus left parenthesis negative 3 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root space equals space square root of 14 comma

the direction-cosines of the line are

fraction numerator 1 over denominator square root of 14 end fraction comma space fraction numerator negative 3 over denominator square root of 14 end fraction comma space fraction numerator 2 over denominator square root of 14 end fraction.