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Question
If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.
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Solution
The direction cosines are given by
`l = a/sqrt(a^2 + b^2 + c^2)`
`m = b/sqrt(a^2 + b^2 + c^2)`
`n = c/sqrt(a^2 + b^2 + c^2)`
Here a, b, c are 1, 1, 2, respectively
Therefore, `l = 1/sqrt(1^2 + 1^2 + 2)`
`m = 1/sqrt(1^2 + 1^2 + 2^2)`
`n = 2/sqrt(1^2 + 1^2 + 2^2)`
i.e., `l = 1/sqrt(6)`
`m = 1/sqrt(6)`
`n = 2/sqrt(6)`
i.e. `+-(1/sqrt(6), 1/sqrt(6), 2/sqrt(6))` are D.C’s of the line.
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