Large reasoning models (LRMs) excel at a long chain of reasoning but often fail to faithfully follow instructions regarding output format, constraints, or specific requirements. We investigate whether this gap can be closed by integrating an instruction-tuned model (ITM) into an LRM. Analyzing their differences in parameter space, namely task vectors, we find that their principal subspaces are nearly orthogonal across key modules, suggesting a lightweight merging with minimal interference. However, we also demonstrate that naive merges are fragile because they overlook the output format mismatch between LRMs (with explicit thinking and response segments) and ITMs (answers-only). We introduce RAIN-Merging (Reasoning-Aware Instruction-attention guided Null-space projection Merging), a gradient-free method that integrates instruction following while preserving thinking format and reasoning performance. First, with a small reasoning calibration set, we project the ITM task vector onto the null space of forward features at thinking special tokens, which preserves the LRM's structured reasoning mechanisms. Second, using a small instruction calibration set, we estimate instruction attention to derive module-specific scaling that amplifies instruction-relevant components and suppresses leakage. Across four instruction-following benchmarks and nine reasoning & general capability benchmarks, RAIN-Merging substantially improves instruction adherence while maintaining reasoning quality. The gains are consistent across model scales and architectures, translating to improved performance in agent settings.