Question:

If a unit vector a makes angles π/3 with î, π/4 with ĵ and θ∈(0,π) with k̂, then a value of θ is:

5π12

5π6

2π3

π4

Correct option is C. 2π3
cos²α + cos²β + cos²γ = 1
1/2 + 1/4 + cos²γ = 1
cos²γ = 1 - 3/4 = 1/4
cos γ = ±1/2
⇒ γ = π/3 or 2π/3