If the sides A B and A C of A B C are represented by vectors j + k and 3 i - j +4 k respectively, then the length of the median through A on BC is:

If the sides $\displaystyle A B$ and $\displaystyle A C$ of $\displaystyle \triangle A B C$ are represented by vectors $\displaystyle \hat{j}+\hat{k}$ and $\displaystyle 3 \hat{i}-\hat{j}+4 \hat{k}$ respectively, then the length of the median through $\displaystyle A$ on BC is :