Vectors - Equations of Lines
Vectors - Equations of Lines
TGM Original Questions
The line \({{l}_{2}}\) passes through \(A\left( 2,-3,2 \right)\) and is parallel to the direction vector \(\left( \begin{matrix} 29 \\-2 \\ 10 \end{matrix} \right)\).
\({{l}_{2}}\) intersects \({{l}_{1}}:\mathbf{r}=\left( \begin{matrix} 1 \\ -5 \\2 \end{matrix} \right)+\lambda \left( \begin{matrix}14 \\-2 \\ 5 \end{matrix} \right);\lambda \in \mathbb{R}\) at \(C\). Find
- the coordinates of \(C\),
- the acute angle between \({{l}_{1}}\) and \({{l}_{2}}\),
- the vector line equation of mirror image of \({{l}_{2}}\) in \({{l}_{1}}\).
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Answer:(i) \(\left( -27,-1,-8 \right)\) (ii) \(4.0{}^\circ\) (iii) \(\mathbf{r}=\left( \begin{matrix}
-27 \\
-1 \\
-8 \\
\end{matrix} \right)+\alpha \left( \begin{matrix}
1271 \\
-278 \\
470 \\
\end{matrix} \right);\alpha \in \mathbb{R}\)
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