Show that lines l1 and l2 intersect and find the coordinate of the point of intersection Q. l1: r = (2i - j + k) + lambda(i + 3j + 2k), l2: r = (2i + 2j + k) + mu(2i - j + k).

Part (i): Show that $l_1$ and $l_2$ intersect and find the coordinate of the point of intersection Q

The equations of the lines are given as:
$l_1: \mathbf{r} = (2\mathbf{i} - \mathbf{j} + \mathbf{k}) + \lambda(\mathbf{i} + 3\mathbf{j} + 2\mathbf{k})$
$l_2: \mathbf{r} = (2\mathbf{i} + 2\mathbf{j} + \mathbf{k}) + \mu(2\mathbf{i} - \mathbf{j} + \mathbf{k})$

Step 1