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Three Dimensional Geometry

Question
CBSEENMA12033258

The equation of a line is given by fraction numerator 4 minus straight x over denominator 2 end fraction space equals space fraction numerator straight y plus 3 over denominator 3 end fraction space equals fraction numerator straight z plus 2 over denominator 6 end fraction. Write the direction cosines of a line parallel to the above line. 

Solution
The equation of given line is
                               fraction numerator 4 minus straight x over denominator 2 end fraction space equals space fraction numerator straight y plus 3 over denominator 2 end fraction space equals space fraction numerator straight z plus 2 over denominator 6 end fraction
or                        fraction numerator straight x minus 4 over denominator negative 2 end fraction space equals space fraction numerator straight y plus 3 over denominator 3 end fraction space equals space fraction numerator straight z plus 2 over denominator 6 end fraction
Its direction ratios are - 2, 3, 6
∴  direction ratios of a line parallel to given line are – 2, 3, 6.
∴  direction cosines of line are       fraction numerator negative 2 over denominator square root of 4 plus 9 plus 36 end root end fraction comma space fraction numerator 3 over denominator square root of 4 plus 9 plus 36 end root end fraction comma space fraction numerator 6 over denominator square root of 4 plus 9 plus 36 end root end fraction space space space straight i. straight e. space space minus fraction numerator 2 over denominator square root of 49 end fraction comma space fraction numerator 3 over denominator square root of 49 end fraction comma space fraction numerator 6 over denominator square root of 49 end fraction
i.e.,   negative 2 over 7 comma space 3 over 7 comma space 6 over 7.