14. As shown in the figure, quadrilaterals $ABCD$ and $ADPQ$ are both squares, and the planes they lie in are mutually perpendicular. A moving point $M$ is on segment $PQ$. $\mathrm { E }$ and $\mathrm { F }$ are the midpoints of $\mathrm { AB }$ and $\mathrm { BC }$ respectively. Let the angle between skew lines $EM$ and $AF$ be $\theta$, then the maximum value of $\cos \theta$ is $\_\_\_\_$. [Figure]

13. As shown in the figure, in the triangular pyramid $A - B C D$, $AB = AC = BD = CD = 3$ , $AD = BC = 2$ , and $M , N$ are the midpoints of $AD , BC$ respectively. Then the cosine of the angle between the skew lines $AN$ and $CM$ is $\_\_\_\_$ .

10. In a right triangular prism $A B C - A _ { 1 } B _ { 1 } C _ { 1 }$, $\angle A B C = 120 ^ { \circ } , A B = 2 , B C = C C _ { 1 } = 1$. The cosine of the angle between skew lines $A B _ { 1 }$ and $B C _ { 1 }$ is
A. $\frac { \sqrt { 3 } } { 2 }$
B. $\frac { \sqrt { 15 } } { 5 }$
C. $\frac { \sqrt { 10 } } { 5 }$
D. $\frac { \sqrt { 3 } } { 3 }$ [Figure]

In the rectangular prism $A B C D - A _ { 1 } B _ { 1 } C _ { 1 } D _ { 1 }$, $E$ is the midpoint of edge $C C _ { 1 }$. The tangent of the angle between skew lines $A E$ and $C D$ is
A. $\frac { \sqrt { 2 } } { 2 }$
B. $\frac { \sqrt { 3 } } { 2 }$
C. $\frac { \sqrt { 5 } } { 2 }$
D. $\frac { \sqrt { 7 } } { 2 }$

In rectangular prism $A B C D - A _ { 1 } B C _ { 1 } D _ { 1 }$, $A B = B C = 1 , A A _ { 1 } = \sqrt { 3 }$, the cosine of the angle between skew lines $A D _ { 1 }$ and $D B _ { 1 }$ is
A. $\frac { 1 } { 5 }$
B. $\frac { \sqrt { 5 } } { 6 }$
C. $\frac { \sqrt { 5 } } { 5 }$
D. $\frac { \sqrt { 2 } } { 2 }$