Two lines $$\(l\)$$ and $$\(m\)$$ have equations $$\(\mathbf{r}=3 \mathbf{i}+2 \mathbf{j}+5 \mathbf{k}+s(4 \mathbf{i}-\mathbf{j}+3 \mathbf{k})\)$$ and $$\(\mathbf{r}=\mathbf{i}-\mathbf{j}-2 \mathbf{k}+t(-\mathbf{i}+2 \mathbf{j}+2 \mathbf{k})\)$$ respectively. Show that $$\(l\)$$ and $$\(m\)$$ are perpendicular. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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