A small underwater research probe is held in equilibrium by three coplanar tension forces: ${\mathbf{T}}_1$, ${\mathbf{T}}_2$, and ${\mathbf{T}}_3$, as shown in the free-body diagram below.

Given that ${\mathbf{T}}_1=-12\mathbf{i}+5\mathbf{j}N$ and ${\mathbf{T}}_2=4\mathbf{i}+10\mathbf{j}N$, find the magnitude of the tension force ${\mathbf{T}}_3$.