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Question
Find the direction cosines of a line which makes equal angles with the coordinate axes.
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Solution
Suppose the line makes an angle a with the directrixes, then their direction cosines:
I = cos α, m = cos α, n = cos α
We know that, l2 + m2 + n2 = 1
cos2 α + cos2 α + cos2 α = 1
3cos2 α = 1
cos2 α = `1/3`
cos α = `± 1/sqrt3`
direction cosines of a line = `< 1/sqrt3, 1/sqrt3, 1/sqrt3 >` and `<-1/sqrt3, -1/sqrt3, -1/sqrt3>`
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