Resonant activation is one of the classical effects demonstrating the constructive role of noise. In resonant activation, the cooperative action of a barrier modulation process and noise lead to the optimal escape kinetics as measured by the mean first passage time. Resonant activation has been observed in versatile systems for various types of barrier modulation process and noise type. Here, we show that resonant activation is also observed in 2D and 3D systems driven by bi-variate and tri-variate α-stable noise. The strength of resonant activation is sensitive to the exact value of the noise parameters. In particular, the decrease in the stability index α results in the disappearance of the resonant activation.