Question

Directional derivative along a line equally inclined with coordinate axis

Answer 1

I think your question is -------> direction cosines and ratio along a line equally inclined with a co-ordinate axes ?

solution :- let inclination angles of line with x -axis , y -axis and z - axis are α , β and γ
we know,
l² + m² + n² = 1 , where l = cosα , m = cosβ and n = cosγ
so, cos²α + cos²β + cos²γ = 1
But according to question,
α = β = γ

∴ cos²α + cos²α + cos²α = 1
⇒ 3cos²α = 1
⇒ cos²α = 1/3
⇒ cosα = ±1/√3

Hence, direction cosines : ±1/√3 , ±1/√3 , ±1/√3
and direction ratio : 1 , 1 , 1