The coordinates of the point where the line joining $P(3, 4, 1)$ and $Q(5, 1, 6)$ crosses the xy-plane are:

$P(3,4,1)$

$Q(5,1,6)$

Equation of PQ

$\cfrac { x-3 }{ 5-3 } =\cfrac { y-4 }{ 1-4 } =\cfrac { z-1 }{ 6-1 } \\ \cfrac { x-3 }{ 2 } =\cfrac { y-4 }{ -3 } =\cfrac { z-1 }{ 5 } \\ In\quad xy\quad plane\quad z=0\\ \therefore \cfrac { z-1 }{ 5 } =\cfrac { -1 }{ 5 } \\ \cfrac { x-3 }{ 2 } =\cfrac { -1 }{ 5 } \\ x=3-\cfrac { 2 }{ 5 } =\cfrac { 13 }{ 5 } \\ \cfrac { y-4 }{ -3 } =\cfrac { -1 }{ 5 } \\ y=4+\cfrac { 3 }{ 5 } =\cfrac { 23 }{ 5 } \\ \therefore Coordinates\quad are\left( \cfrac { 13 }{ 5 } ,\cfrac { 23 }{ 5 } ,0 \right) \\ \\$