11 The lines \(l _ { 1 } , l _ { 2 }\) and \(l _ { 3 }\) are defined as follows.
$$\begin{aligned}
& l _ { 1 } : \left( \mathbf { r } - \left[ \begin{array} { c }
1
5
- 1
\end{array} \right] \right) \times \left[ \begin{array} { c }
- 2
1
- 3
\end{array} \right] = \mathbf { 0 }
& l _ { 2 } : \left( \mathbf { r } - \left[ \begin{array} { c }
- 3
2
7
\end{array} \right] \right) \times \left[ \begin{array} { c }
2
- 1
3
\end{array} \right] = \mathbf { 0 }
& l _ { 3 } : \left( \mathbf { r } - \left[ \begin{array} { c }
- 5
12
- 4
\end{array} \right] \right) \times \left[ \begin{array} { l }
4
0
9
\end{array} \right] = \mathbf { 0 }
\end{aligned}$$
11
- Explain how you know that two of the lines are parallel.
| 11- (ii)
| | Show that the perpendicular distance between these two parallel lines is 7.95 units, correct to three significant figures. | | [5 marks] \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) |
|
| |
- Show that the lines \(l _ { 1 }\) and \(l _ { 3 }\) meet, and find the coordinates of their point of intersection.
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