These Ten-Year-Series (TYS) worked solutions with video explanations for 2016 A Level H2 Mathematics Paper 1 Question 11 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2016 A Level H2 Math Paper 1 Question 11
The plane $p$ has equation $\mathbf{r}=\left( \begin{matrix}
1 \\
-3 \\
2 \\
\end{matrix} \right)+\lambda \left( \begin{matrix}
1 \\
2 \\
0 \\
\end{matrix} \right)+\mu \left( \begin{matrix}
a \\
4 \\
-2 \\
\end{matrix} \right)$ , and the line $l$ has equation $\mathbf{r}=\left( \begin{matrix}
a-1 \\
a \\
a+1 \\
\end{matrix} \right)+t\left( \begin{matrix}
-2 \\
1 \\
2 \\
\end{matrix} \right)$, where $a$ is a constant and $\lambda $, $\mu $ and $t$ are parameters.
(i)
In the case where $a=0$,
(i) In the case where $a=0$,
(a) show that $l$ is perpendicular to $p$ and find the values of $\lambda $, $\mu $ and $t$ which give the coordinates of the point at which $l$ and $p$ intersect,
[5]
(a) show that $l$ is perpendicular to $p$ and find the values of $\lambda $, $\mu $ and $t$ which give the coordinates of the point at which $l$ and $p$ intersect,
[5]
(b) find the Cartesian equations of the planes such that the perpendicular distance from each plane to $p$ is $12$.
[5]
(b) find the Cartesian equations of the planes such that the perpendicular distance from each plane to $p$ is $12$.
[5]
(ii)
Find the value of $a$ such that $l$ and $p$ do not meet in a unique point.
[3]
(ii) Find the value of $a$ such that $l$ and $p$ do not meet in a unique point.
[3]
Suggested Video Solutions
Suggested Handwritten Solutions
Share with your friends!