15 The points \(A ( 7,2,8 ) , B ( 7 , - 4,0 )\) and \(C ( 3,3.2,9.6 )\) all lie in the plane \(\Pi\).
15
- Find a Cartesian equation of the plane \(\Pi\).
15 - The line \(L _ { 1 }\) has equation \(\mathbf { r } = \left[ \begin{array} { c } 5
- 0.4
4.8 \end{array} \right] + \mu \left[ \begin{array} { c } 15
3
4 \end{array} \right]\)
15 - Show that \(L _ { 1 }\) lies in the plane \(\Pi\).
15
- (ii) Show that every point on \(L _ { 1 }\) is equidistant from \(B\) and \(C\).
15 - The line \(L _ { 2 }\) lies in the plane \(\Pi\), and every point on \(L _ { 2 }\) is equidistant from \(A\) and \(B\).
15 - The points \(A , B\) and \(C\) all lie on a circle \(G\). The point \(D\) is the centre of circle \(G\).
Find the coordinates of \(D\).
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