This research presents an innovative methodology aimed at monitoring jet trajectory during the jetting process using imagery captured by unmanned aerial vehicles (UAVs). This approach seamlessly integrates UAV imagery with an offline learnable prompt vector module (OPVM) to enhance trajectory monitoring accuracy and stability. By leveraging a high-resolution camera mounted on a UAV, image enhancement is proposed to solve the problem of geometric and photometric distortion in jet trajectory images, and the Faster R-CNN network is deployed to detect objects within the images and precisely identify the jet trajectory within the video stream. Subsequently, the offline learnable prompt vector module is incorporated to further refine trajectory predictions, thereby improving monitoring accuracy and stability. In particular, the offline learnable prompt vector module not only learns the visual characteristics of jet trajectory but also incorporates their textual features, thus adopting a bimodal approach to trajectory analysis. Additionally, OPVM is trained offline, thereby minimizing additional memory and computational resource requirements. Experimental findings underscore the method's remarkable precision of 95.4% and efficiency in monitoring jet trajectory, thereby laying a solid foundation for advancements in trajectory detection and tracking. This methodology holds significant potential for application in firefighting systems and industrial processes, offering a robust framework to address dynamic trajectory monitoring challenges and augment computer vision capabilities in practical scenarios.