Cambridge AS & A Level. 2025. Mathematics (9709). May/June - Paper 3 (31) · Pure Mathematics 3 - Question 12

With respect to the origin $O$, the points $A$ and $B$ have position vectors $2\mathbf{i}+4\mathbf{k}$ and $5\mathbf{i}+\mathbf{j}+6\mathbf{k}$ respectively. The line $l_1$ passes through the points $A$ and $B$.

**(a)** Find a vector equation for the line $l_1$.