11. Relative to a fixed origin \(O\), the line \(l _ { 1 }\) is given by the equation
$$l _ { 1 } : \quad \mathbf { r } = \left( \begin{array} { r }
2
3
- 1
\end{array} \right) + \lambda \left( \begin{array} { r }
- 1
4
3
\end{array} \right)$$
where \(\lambda\) is a scalar parameter.
The line \(l _ { 2 }\) passes through the origin and is parallel to \(l _ { 1 }\)
- Find a vector equation for \(l _ { 2 }\)
The point \(A\) and the point \(B\) both lie on \(l _ { 1 }\) with parameters \(\lambda = 0\) and \(\lambda = 3\) respectively.
Write down - the coordinates of \(A\),
- the coordinates of \(B\).
- Find the size of the acute angle between \(O A\) and \(l _ { 1 }\)
Give your answer in degrees to one decimal place.
The point \(D\) lies on \(l _ { 2 }\) such that \(O A B D\) is a parallelogram.
- Find the area of \(O A B D\), giving your answer to the nearest whole number.