In a cube $A B C D - A _ { 1 } B _ { 1 } C _ { 1 } D _ { 1 }$ with edge length 10, $P$ is a point on the left face $A D D _ { 1 } A _ { 1 }$. Given that the distance from point $P$ to $A _ { 1 } D _ { 1 }$ is 3 and the distance from point $P$ to $A A _ { 1 }$ is 2, a line through point $P$ parallel to $A _ { 1 } C$ intersects the cube at points $P$ and $Q$. On which face of the cube is point $Q$ located? ( ) A. $A A _ { 1 } B _ { 1 } B$ B. $B B _ { 1 } C _ { 1 } C$ C. $C C _ { 1 } D _ { 1 } D$ D. $A B C D$
In a cube $A B C D - A _ { 1 } B _ { 1 } C _ { 1 } D _ { 1 }$ with edge length 10, $P$ is a point on the left face $A D D _ { 1 } A _ { 1 }$. Given that the distance from point $P$ to $A _ { 1 } D _ { 1 }$ is 3 and the distance from point $P$ to $A A _ { 1 }$ is 2, a line through point $P$ parallel to $A _ { 1 } C$ intersects the cube at points $P$ and $Q$. On which face of the cube is point $Q$ located? ( )
A. $A A _ { 1 } B _ { 1 } B$
B. $B B _ { 1 } C _ { 1 } C$
C. $C C _ { 1 } D _ { 1 } D$
D. $A B C D$