Question -
Answer -
Given:
Angles are equal.
So let the angles be α, β, γ
Let the direction cosines of the line be l, m and n
l = cos α, m = cos β and n = cos γ
Here given α = β = γ (Since, line makes equal angles with thecoordinate axes) … (1)
The 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
Cos α = ± √(1/3)
∴ The directioncosines are
l = ± √(1/3), m= ± √(1/3), n = ± √(1/3)