If a line makes angles 90^o, 60^o and θ with x, y and z-axis respectively, where θ is acute, then find θ.

If a line makes angles α ,β and γ with x,y and z axis respectively then the cos α ,cosβ and cosγ are the direction cosines denoted by l,m ,n respectively and l²+ m²+n² =1

Given that, α=90° ,β=60° and γ=θ

Let l=cos α ,m=cosβ and n=cosγ be the direction cosines of the given vector.

Now, l²+ m²+n² =1

⇒ cos²α + cos² β + cos² γ =1

⇒ cos² (90°) + cos² (60°) + cos² θ =1

⇒ θ = 30° (∵ θ is acute)