你是一位数学老师，需要给学生进校这个题目的讲解，麻烦给出一个讲解视频，逐一对每个选项进行分析，给出正确的答案。---**Question Stem:** 如图, 已知边长为 6 的正方形 ABCD 和正方形 ADEF 所在的平面互相垂直, O 是 BE 的中点, $\vec{FM} = \frac{1}{2}\vec{MA}$, 则线段 OM 的长为 **Mathematical Formulas/Equations:** $\vec{FM} = \frac{1}{2}\vec{MA}$ **Options:** A. $3\sqrt{2}$ B. $\sqrt{19}$ C. $2\sqrt{5}$ D. $\sqrt{21}$ **Chart/Diagram Description:** * **Type:** 3D geometric figure illustrating two squares sharing a common side and lying in perpendicular planes, with additional points and lines marked. * **Main Elements:** * **Points:** Labeled points A, B, C, D, E, F, M, O. * **Shapes:** Square ABCD and Square ADEF are shown. They share the side AD. * **Lines:** Lines connecting points are shown as edges or segments. These include edges of the squares (AB, BC, CD, DA, AE, EF, FD), the diagonal BE of the figure formed by points A, B, E, D, and segments MO and AO (implied or useful for analysis). The segment BE is explicitly marked with its midpoint O. The segment AF is marked with point M. A line segment is drawn connecting M and O. * **Relative Position and Direction:** Square ABCD appears to be in a horizontal plane, while square ADEF appears to be in a vertical plane perpendicular to the horizontal plane, with AD as the common edge. Point E is above point A. Point F is above point D. Point B is to the right of A. Point C is to the right of B. Point M is located on the segment AF. Point O is located on the segment BE. A line segment connects M and O. * **Labels and Annotations:** Points are labeled with capital letters. The length of the side of the squares is given as 6 in the problem description. O is labeled as the midpoint of BE. M is labeled on AF, related by the vector equation $\vec{FM} = \frac{1}{2}\vec{MA}$.