Detecting hallucinations in large language models (LLMs) is critical for their safety in many applications. Without proper detection, these systems often provide harmful, unreliable answers. In recent years, LLMs have been actively used in retrieval-augmented generation (RAG) settings. However, hallucinations remain even in this setting, and while numerous hallucination detection methods have been proposed, most approaches are not specifically designed for RAG systems. To overcome this limitation, we introduce a hallucination detection method based on estimating the distances between the distributions of prompt token embeddings and language model response token embeddings. The method examines the geometric structure of token hidden states to reliably extract a signal of factuality in text, while remaining friendly to long sequences. Extensive experiments demonstrate that our method achieves state-of-the-art or competitive performance. It also has transferability from solving the NLI task to the hallucination detection task, making it a fully unsupervised and efficient method with a competitive performance on the final task.