Vectors - Perpendicular Projection and Reflection in a Plane
Vectors - Perpendicular Projection and Reflection in a Plane
TGM Original Questions
The line \({{l}_{3}}\) which passes through \(B(3,-4,4)\) and is parallel to the direction vector \(\left( \begin{matrix}14 \\ -2 \\5 \end{matrix} \right)\).
The plane \({{p}_{1}}\) has the equation \({{p}_{1}}:3x-2y-3z=4\). 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 \({{p}_{1}}\).
Video Solution:
Video solution locked
Solution:
Solution locked
Sign in to view the step-by-step solution
Similar questions are unavailable for this question.
Answer:(i) \(\left( \frac{79}{31},-\frac{122}{31},\frac{119}{31} \right)\) (ii) \(26.1{}^\circ\) (iii) \(\mathbf{r}=\frac{1}{11}\left( \begin{matrix}
30 \\
-42 \\
47 \\
\end{matrix} \right)+\beta \left( \begin{matrix}
61 \\
40 \\
148 \\
\end{matrix} \right);\beta \in \mathbb{R}\)
Need help? Join our JC Math tuition classes.
Learn more