Vectors - Intersection of a Line and a Plane
Vectors - Intersection of a Line and a Plane
TGM Original Questions
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
- the coordinates of point of intersection between the line \({{l}_{3}}\) and plane \({{p}_{1}}\),
- the acute angle between the line \({{l}_{3}}\) and plane \({{p}_{1}}\),
- the equation of line of the image of line \({{l}_{3}}\) in plane \({{p}_{1}}\).
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Answer:(i) \(\left( \frac{57}{11},\frac{24}{11},-\frac{20}{11} \right)\) (ii) \(40.8{}^\circ\) (iii) \(\mathbf{r}=\frac{1}{7}\left( \begin{matrix}
59 \\
-2 \\
-15 \\
\end{matrix} \right)+\beta \left( \begin{matrix}
50 \\
-38 \\
-5 \\
\end{matrix} \right);\beta \in \mathbb{R}\)
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