Unit 13.2 Worked Example 4

Unit 13.2 Worked Example 4

TGM Original Questions
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The line \({{l}_{3}}\) which passes through \(B\left( 7,4,-5 \right)\) and is parallel to the direction vector \(\left( \begin{matrix}4 \\4 \\-7 \end{matrix} \right)\). The plane \({{p}_{1}}\) has the equation \(x-3y+2z=-5\). Find

  1. the coordinates of point of intersection between the line \({{l}_{3}}\) and plane \({{p}_{1}}\),
  2. the acute angle between the line \({{l}_{3}}\) and plane \({{p}_{1}}\),
  3. the equation of line of the image of line \({{l}_{3}}\) in plane \({{p}_{1}}\).

Video Solution:

Default solution

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Answer:(i) \(\left(\displaystyle\frac{57}{11}, \frac{24}{11}, -\frac{20}{11}\right)\); (ii) \(40.8^\circ\); (iii) \(\mathbf{r} = \displaystyle\frac{1}{11}\begin{pmatrix} 57 \\\\ 24 \\\\ -20 \end{pmatrix} + t\begin{pmatrix} 50 \\\\ -38 \\\\ -5 \end{pmatrix}\)

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