12 The line \(L _ { 1 }\) has equation
$$\mathbf { r } = \left[ \begin{array} { l }
4
2
1
\end{array} \right] + \lambda \left[ \begin{array} { r }
1
3
- 1
\end{array} \right]$$
The transformation T is represented by the matrix
$$\left[ \begin{array} { c c c }
2 & 1 & 0
3 & 4 & 6
- 5 & 2 & - 3
\end{array} \right]$$
The transformation T transforms the line \(L _ { 1 }\) to the line \(L _ { 2 }\)
12
- Show that the angle between \(L _ { 1 }\) and \(L _ { 2 }\) is 0.701 radians, correct to three decimal places.
[0pt]
[4 marks]
| 12 | | Find the shortest distance between \(L _ { 1 }\) and \(L _ { 2 }\) | | Give your answer in an exact form. |
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