(i)[5]
Find the value of $p$ and the coordinates of the point where the lines intersect.
(ii)[5]
Find the equation of the plane that contains the two lines, and give your answer in the form $ax+by+cz=d$, where $a$, $b$, $c$ and $d$ are integers.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The equations of the two lines are $\mathbf{r}=\begin{pmatrix}5\\1\\-4\end{pmatrix}+s\begin{pmatrix}1\\-1\\3\end{pmatrix}$ and $\mathbf{r}=\begin{pmatrix}p\\4\\-2\end{pmatrix}+t\begin{pmatrix}2\\5\\-4\end{pmatrix}$, with $p$ being a constant. It is stated that the lines intersect.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A general point on either line has coordinates $(5+s,1-s,-4+3s)$ or $(p+2t,4+5t,2-4t)$” …
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