Three Dimensional Geometry

Consider the lines $L_1$ and $L_2$ given by the following vector equations:

\(L_1: \vec{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda(3 \hat{i}+\boldsymbol{t} \hat{j}) \quad L_2: \vec{r}=(4 \hat{i}+\boldsymbol{a} \hat{j}-\hat{k})+\mu(2 \hat{i}+3 \hat{k})\)

If $\boldsymbol{a}=-2$ and the lines intersect, then the value of ' $\mathbf{t}$ ' is: