The point $L$, which lies vertically above the midpoint of the edge $\left[ \mathrm { A } _ { 1 } \mathrm {~A} _ { 2 } \right]$, represents the position of a floodlight in the model, which is installed 12 m above the base. The points $L , B _ { 2 }$ and $B _ { 3 }$ determine a plane $F$. Find an equation of $F$ in normal form.
(for verification: $F : 3 x _ { 1 } + x _ { 2 } + 5 x _ { 3 } - 90 = 0$ )