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Three Dimensional Geometry

Question

If a line has the direction ratios – 18, 12, – 4. then what are its direction cosines?

Solution

Direction ratios of the line are – 18, 12, –4
Dividing each by

square root of left parenthesis negative 18 right parenthesis squared plus left parenthesis 12 right parenthesis squared plus left parenthesis negative 4 right parenthesis squared end root space equals space square root of 324 plus 144 plus 16 end root space equals square root of 484 space equals space 22 comma

the direction cosines of the line are

negative 18 over 22 comma space 12 over 22 comma space fraction numerator negative 4 over denominator 22 end fraction space straight i. straight e. space minus 9 over 11 comma space 6 over 11 comma space minus 2 over 11.