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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"62)`
Here a, b, c are 1, 1, 2, respectively
Therefore, l = `1/sqrt(1^2 + 1^2 + 2^2)`
m = `1/sqrt(1^2 + 1^2 + 2^2)`
n = `"c"/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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