Q. 24.4( 53 Votes )
Find the direction cosines of a line which makes equal angles with the coordinate axes.
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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