1. Vector: Lines Intersect

Vectors have to be my weakest points. How would I do this question, will I need to find $\displaystyle s$ and $\displaystyle t$? Help would be appreciated.

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Q:

Referred to a fixed origin $\displaystyle O$, the lines $\displaystyle l_1$ and $\displaystyle l_2$ have equations $\displaystyle \bold r = 3 \bold i + 6 \bold j + \bold k + s (2 \bold i + 3 \bold j - \bold k)$ and $\displaystyle \bold r = 3 \bold i - \bold j + 4 \bold k + t ( \bold i -2 \bold j + \bold k)$ respectively, where $\displaystyle s$ and $\displaystyle t$ are scalar parameters.

Show that $\displaystyle l_1$ and $\displaystyle l_2$ intersect and determine the position vector of their point of intersection.

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2. Rewrite the lines as: $\displaystyle l_1 = \left\{ \begin{array}{r} 3 + 2s \\ 6 + 3s \\ 1 - s \\ \end{array} \right.\quad ,\quad l_2 = \left\{ \begin{array}{r} 3 + t \\ - 1 - 2t \\ 4 + t \\ \end{array} \right.$