For the cross product vector a⃗ × b⃗ to be a unit vector, its magnitude must equal 1. The magnitude of a cross product is given by |a⃗ × b⃗| = |a⃗| |b⃗| sin θ, where θ is the angle between the two vectors. Given |a⃗| = 3 and |b⃗| = $\sqrt{2}$/3, we set up the equation: 3 × ($\sqrt{2}$/3) × sin θ = 1, which simplifies to $\sqrt{2}$ × sin θ = 1, giving sin θ = 1/$\sqrt{2}$. Since sin(π/4) = 1/$\sqrt{2}$, the angle between the vectors must be π/4.