(i)[2]
Assuming that $l$ is not contained in $p$, show that $l$ is parallel to $p$.
(ii)[2]
Determine the value of $a$ for which $l$ lies in $p$.
(iii)[5]
It is now stated that the distance between $l$ and $p$ is 6. Find the possible values of $a$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The line $l$ is given by $\mathbf{r} = \begin{pmatrix} a \\ 1 \\ 4 \end{pmatrix} + \lambda \begin{pmatrix} 4 \\ 3 \\ -2 \end{pmatrix}$, with $a$ as a constant. The plane $p$ is defined by $2x - 2y + z = 10$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Calculate the scalar product of the direction of $l$ and the normal to $p$” …
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