Unit 13.2 Worked Example 2

Unit 13.2 Worked Example 2

TGM Original Questions
Free

The line \({{l}_{2}}\) passes through \(A\left( 3,1,-2 \right)\) and is parallel to the direction vector \(\left( \begin{matrix}7  \\15  \\1  \end{matrix} \right)\).

\({{l}_{2}}\) intersects \({{l}_{1}}:\mathbf{r}=\left( \begin{matrix}  -12  \\ -22  \\ 11  \end{matrix} \right)+\lambda \left( \begin{matrix}4  \\ 4  \\ -7  \end{matrix} \right);\lambda \in \mathbb{R}\) at \(C\).Find

  1. the coordinates of \(C\),
  2. the acute angle between \({{l}_{1}}\) and \({{l}_{2}}\),
  3. the vector line equation of mirror image of \({{l}_{2}}\) in \({{l}_{1}}\).

Video Solution:

Default solution

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Answer:(i) \(C=(-4,-14,-3)\). (ii) \(57.1^\circ\). (iii) \(\mathbf r=\begin{pmatrix}-4\\-14\\-3\end{pmatrix}+\alpha\begin{pmatrix}-1\\7\\15\end{pmatrix},\ \alpha\in\mathbb R\).

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