11 The line \(l _ { 1 }\) passes through the points \(A ( 2,3 , - 5 )\) and \(B ( 8,7 , - 13 )\). The line \(l _ { 2 }\) passes through the points \(C ( - 2,1,8 )\) and \(D ( 3 , - 1,4 )\). Find the shortest distance between the lines \(l _ { 1 }\) and \(l _ { 2 }\). The plane \(\Pi _ { 1 }\) passes through the points \(A , B\) and \(D\). The plane \(\Pi _ { 2 }\) passes though the points \(A , C\) and \(D\). Find the acute angle between \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\), giving your answer in degrees.

11 The line $l _ { 1 }$ passes through the points $A ( 2,3 , - 5 )$ and $B ( 8,7 , - 13 )$. The line $l _ { 2 }$ passes through the points $C ( - 2,1,8 )$ and $D ( 3 , - 1,4 )$. Find the shortest distance between the lines $l _ { 1 }$ and $l _ { 2 }$.

The plane $\Pi _ { 1 }$ passes through the points $A , B$ and $D$. The plane $\Pi _ { 2 }$ passes though the points $A , C$ and $D$. Find the acute angle between $\Pi _ { 1 }$ and $\Pi _ { 2 }$, giving your answer in degrees.

\hfill \mbox{\textit{CAIE FP1 2014 Q11}}