Question 6 6 marks Paper 2 Section A Medium Calculator Free
Maximum mark: 6
A line \( L_{1} \) has equation
\[ \mathbf{r} = \begin{pmatrix} -5 \\ -3 \\ 2 \end{pmatrix} + \lambda\begin{pmatrix} -1 \\ 2 \\ 2 \end{pmatrix}. \]
A line \( L_{2} \) passing through the origin intersects \( L_{1} \) and is perpendicular to \( L_{1} \).
(a) Find a vector equation of \( L_{2} \).[4]
(b) Determine the shortest distance from the origin to \( L_{1} \).[2]
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