4. The plane \(\Pi\) has equation
$$\mathbf { r } = \left( \begin{array} { l }
3
3
2
\end{array} \right) + \lambda \left( \begin{array} { r }
- 1
2
1
\end{array} \right) + \mu \left( \begin{array} { l }
2
0
1
\end{array} \right)$$
where \(\lambda\) and \(\mu\) are scalar parameters.
- Show that vector \(2 \mathbf { i } + 3 \mathbf { j } - 4 \mathbf { k }\) is perpendicular to \(\Pi\).
- Hence find a Cartesian equation of \(\Pi\).
The line \(l\) has equation
$$\mathbf { r } = \left( \begin{array} { r }
4
- 5
2
\end{array} \right) + t \left( \begin{array} { r }
1
6
- 3
\end{array} \right)$$
where \(t\) is a scalar parameter.
The point \(A\) lies on \(l\).
Given that the shortest distance between \(A\) and \(\Pi\) is \(2 \sqrt { 29 }\) - determine the possible coordinates of \(A\).
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