If a unit vector makes angle π/3 with ^i, π/4 with ^j and an acute angle θ with ^k, then find the value of θ.

Let α be an angle formed by vector with i and β be an angle formed by j and θ be an angle formed by vector k.
Now as rule states, cos²α + cos²β + cos²θ = 1
⇒cos²(π/3) + cos²(π/4) + cos²θ = 1
⇒(1/4) + (1/2) + cos²θ = 1
cos²θ = 1 - (1/4) - (1/2) = 1/4
cos θ = √(1/4) = 1/2
Therefore, θ = cos⁻¹(1/2) = π/3