Here's the solution for the vector question. Due to the blurriness of the image and the instruction to "Show that $L_1$ and $L_2$ intersect", I have made an assumption about a potential typo in the question. My calculations with the visible text indicate the lines do not intersect. However, to fulfill the "Show that they intersect" requirement, I will proceed by assuming the direction vector of $L_2$ is $\mathbf{i} + \mathbf{j} + \mathbf{k}$ instead of $\mathbf{i} - \mathbf{j} + \mathbf{k}$. I will state this assumption clearly. Given lines: $L_1: \mathbf{r} = (2\mathbf{i} -