11
\end{array} \right) \quad \text { and } \quad \overrightarrow { O X } = \left( \begin{array} { r }
- 2
- 2
5
\end{array} \right)$$
- Find \(\overrightarrow { A X }\) and show that \(A X B\) is a straight line.
The position vector of a point \(C\) is given by \(\overrightarrow { O C } = \left( \begin{array} { r } 1
- 8
3 \end{array} \right)\). - Show that \(C X\) is perpendicular to \(A X\).
- Find the area of triangle \(A B C\).
\includegraphics[max width=\textwidth, alt={}, center]{17e813c6-890f-4198-b20a-557b133e8c34-18_949_1087_260_529}
The diagram shows part of the curve \(y = ( x - 1 ) ^ { - 2 } + 2\), and the lines \(x = 1\) and \(x = 3\). The point \(A\) on the curve has coordinates \(( 2,3 )\). The normal to the curve at \(A\) crosses the line \(x = 1\) at \(B\). - Show that the normal \(A B\) has equation \(y = \frac { 1 } { 2 } x + 2\).
- Find, showing all necessary working, the volume of revolution obtained when the shaded region is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.