The quadrilateral $$\(A B C D\)$$ is a trapezium in which $$\(A B\)$$ and $$\(D C\)$$ are parallel. With respect to the origin $$\(O\)$$, the position vectors of $$\(A, B\)$$ and $$\(C\)$$ are given by $$\(\overrightarrow{O A}=-\mathbf{i}+2 \mathbf{j}+3 \mathbf{k}, \overrightarrow{O B}=\mathbf{i}+3 \mathbf{j}+\mathbf{k}\)$$ and  $$\(\overrightarrow{O C}=2 \mathbf{i}+2 \mathbf{j}-3 \mathbf{k}\)$$ State a vector equation for the line through $$\(A\)$$ and $$\(B\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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