(i)[4]
Show that the two lines intersect for every value of $a$.
(ii)[4]
If the intersection point is $9$ units from the origin, determine the possible values of $a$.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
The two straight lines are given by $\mathbf{r} = \mathbf{i} + 4\mathbf{j} - 2\mathbf{k} + \lambda(\mathbf{i} + 3\mathbf{k})$ and $\mathbf{r} = a\mathbf{i} + 2\mathbf{j} - 2\mathbf{k} + \mu(\mathbf{i} + 2\mathbf{j} + 3a\mathbf{k})$, where $a$ is a constant.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State any two of the equations $1+\lambda=a+\mu$, $4=2+2\mu$, $-2+3\lambda=-2+3a\mu$” …
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