Question 13
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 $B$.
The line $l_2$ has equation $\mathbf{r} = 2\mathbf{i}+\mathbf{j}+5\mathbf{k}+\mu(\mathbf{i}+2\mathbf{j}+3\mathbf{k})$.
(In part (a) you found $l_1$: $\mathbf{r} = 2\mathbf{i}+4\mathbf{k}+\lambda(3\mathbf{i}+\mathbf{j}+2\mathbf{k})$.)
**(b)** Show that $l_1$ and $l_2$ do **not** intersect.
The line $l_2$ has equation $\mathbf{r} = 2\mathbf{i}+\mathbf{j}+5\mathbf{k}+\mu(\mathbf{i}+2\mathbf{j}+3\mathbf{k})$.
(In part (a) you found $l_1$: $\mathbf{r} = 2\mathbf{i}+4\mathbf{k}+\lambda(3\mathbf{i}+\mathbf{j}+2\mathbf{k})$.)
**(b)** Show that $l_1$ and $l_2$ do **not** intersect.
