10 Point A has position vector \(\left( \begin{array} { l } a
b
0 \end{array} \right)\) where \(a\) and \(b\) can vary, point B has position vector \(\left( \begin{array} { l } 4
2
0 \end{array} \right)\) and point C has position vector \(\left( \begin{array} { l } 2
4
2 \end{array} \right)\). ABC is an isosceles triangle with \(\mathrm { AC } = \mathrm { AB }\).
- Show that \(a - b + 1 = 0\).
- Determine the position vector of A such that triangle ABC has minimum area.
Answer all the questions.
Section B (15 marks)
The questions in this section refer to the article on the Insert. You should read the article before attempting the questions.