The task of Information Retrieval (IR) requires a system to identify relevant documents based on users' information needs. In real-world scenarios, retrievers are expected to not only rely on the semantic relevance between the documents and the queries but also recognize the nuanced intents or perspectives behind a user query. For example, when asked to verify a claim, a retrieval system is expected to identify evidence from both supporting vs. contradicting perspectives, for the downstream system to make a fair judgment call. In this work, we study whether retrievers can recognize and respond to different perspectives of the queries -- beyond finding relevant documents for a claim, can retrievers distinguish supporting vs. opposing documents? We reform and extend six existing tasks to create a benchmark for retrieval, where we have diverse perspectives described in free-form text, besides root, neutral queries. We show that current retrievers covered in our experiments have limited awareness of subtly different perspectives in queries and can also be biased toward certain perspectives. Motivated by the observation, we further explore the potential to leverage geometric features of retriever representation space to improve the perspective awareness of retrievers in a zero-shot manner. We demonstrate the efficiency and effectiveness of our projection-based methods on the same set of tasks. Further analysis also shows how perspective awareness improves performance on various downstream tasks, with 4.2% higher accuracy on AmbigQA and 29.9% more correlation with designated viewpoints on essay writing, compared to non-perspective-aware baselines.