Answer :

Let the direction cosines of the line making α with x-axis, β – with y axis and γ- with z axis are l, m and n

l = cos α, m = cos β and n = cos γ

Here given α = β = γ (line makes equal angles with the coordinate axes) ……….1

Direction Cosines are

l = cos α, m = cos β and n = cos γ

We have

l2 + m 2 + n2 = 1

cos2 α + cos2β + cos2γ = 1

From 1 we have

cos2 α + cos2 α + cos2 α = 1

3 cos2 α = 1

The direction cosines are

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