第14道题怎么做---Here is the extraction of the content from the image: **Geometry Diagram Description:** * Type: Perspective drawing of a geometric figure, appearing to be part of a prism or parallelepiped. * Elements: * Vertices labeled A, B, C, D, A₁, P. * Edges shown as solid lines (A₁A, A₁D₁, A₁B₁, AB, AD, BB₁, DD₁, CB, CD) and dashed lines (A₁D₁, A₁B₁, CD). * Points A, B, C, D form a base (presumably) with A₁ above A. * Point P appears to be above C. * A dashed line connects P to A₁, indicating a diagonal or internal line. * The figure seems to depict part of a parallelepiped ABCD-A₁B₁C₁D₁, with P being a vertex or point related to the top face. However, the diagram is only partially visible and labeled. **Multiple Choice Questions (Partial):** * B. 若 AQ = $\sqrt{5}$ ,则点 Q 的轨迹为一段圆弧 * C. 若 $\triangle A_{1}BQ$ 的外心为 O, 则 $\vec{AB} \cdot \vec{AO}$ 为定值 2 * D. 若 $\lambda = 1$ 且 $\mu = \frac{1}{2}$ ,则存在点 E $\in$ AB, 使得 AE + EQ 的最小值为 $\sqrt{9+2\sqrt{10}}$ **Fill-in-the-blank Questions:** * 三、填空题 * 12. 若 $\vec{a}, \vec{b}, \vec{c}$ 为空间两两夹角都是 $120^\circ$ 的三个单位向量, 则 $|\vec{a}-2\vec{b}+\vec{c}| = \underline{\quad}$. * 13. 已知 $\vec{a}=(1,0,2), \vec{b}=(-5,2,3)$, 则向量 $\vec{b}$ 在向量 $\vec{a}$ 上的投影向量是 $\underline{\quad}$. (Note: The handwritten answer is visible: $(-\frac{1}{2}, 0, -1)$ ) * 14. 在平行六面体 $ABCD-A_{1}B_{1}C_{1}D_{1}$ 中, $AD=4, AA_{1}=6, AB=2, \angle DAB=60^\circ, \angle A_{1}AD=60^\circ, \angle A_{1}AB=60^\circ$, 则 $|\vec{BD_{1}}| = \underline{\quad}$. **Other Text:** * 共 2页 (Total 2 pages)