These Ten-Year-Series (TYS) worked solutions with video explanations for 2017 A Level H2 Mathematics Paper 1 Question 10 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2017 A Level H2 Math Paper 1 Question 10
Electrical engineers are installing electricity cables on a building site. Points $(x,y,z)$ are defined relative to a main switching site at $(0,0,0)$, where units are metres. Cables are laid in straight lines and the widths of cables can be neglected.
An existing cable $C$ starts at the main switching site and goes in the direction $\left( \begin{matrix}3 \\1 \\-2 \\\end{matrix} \right)$. A new cable is installed which passes through points $P\,(1,2-1)$ and $Q\,(5,7,a)$.
(i)
Find the value of $a$ for which $C$ and the new cable will meet.
[4]
(i) Find the value of $a$ for which $C$ and the new cable will meet.
[4]
To ensure that the cables do not meet, the engineers use $a=-3$. The engineers wish to connect each of the points $P$ and $Q$ to a point $R$ on $C$.
(ii)
The engineers wish to reduce the length of cable required and believe in order to do this that angle $PRQ$ should be $90{}^\circ $. Show that this is not possible.
[4]
(ii) The engineers wish to reduce the length of cable required and believe in order to do this that angle $PRQ$ should be $90{}^\circ $. Show that this is not possible.
[4]
(iii)
The engineers discover that the ground between $P$ and $R$ is difficult to drill through and now decide to make the length of $PR$ as small as possible. Find the coordinates of $R$ in this case and the exact minimum length.
[5]
(iii) The engineers discover that the ground between $P$ and $R$ is difficult to drill through and now decide to make the length of $PR$ as small as possible. Find the coordinates of $R$ in this case and the exact minimum length.
[5]
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