The point $T ( 7 | 10 | 0 )$ lies on the edge $\left[ \mathrm { A } _ { 3 } \mathrm {~A} _ { 4 } \right]$. Investigate computationally whether there are points on the edge $\left[ \mathrm { B } _ { 3 } \mathrm {~B} _ { 4 } \right]$ for which the following holds: The line segments connecting the point to the points $B _ { 1 }$ and $T$ are perpendicular to each other. If applicable, give the coordinates of these points.