Continuum robots are compact and flexible, making them suitable for use in the industries and in medical surgeries. Rapidly-exploring random trees (RRT) are a highly efficient path planning method, and its variant, S-RRT, can generate smooth feasible paths for the end-effector. By combining RRT with inverse instantaneous kinematics (IIK), complete motion planning for the continuum arm can be achieved. Due to the high degrees of freedom of continuum arms, the null space in IIK can be utilized for obstacle avoidance. In this work, we propose a novel approach that uses the S-RRT* algorithm to create paths for the continuum-rigid manipulator. By employing IIK and null space techniques, continuous joint configurations are generated that not only track the path but also enable obstacle avoidance. Simulation results demonstrate that our method effectively handles motion planning and obstacle avoidance while generating high-quality end-effector paths in complex environments. Furthermore, compared to similar IIK methods, our approach exhibits superior computation time.