Vectors - Perpendicular Projection and Reflection in a Line
Vectors - Perpendicular Projection and Reflection in a Line
TGM Original Questions
The equation of line \({{l}_{1}}\) is given by \(\mathbf{r}=\left( \begin{matrix} 1 \\ -5 \\ 2 \end{matrix} \right)+\lambda \left( \begin{matrix} 14 \\ -2 \\ 5 \end{matrix} \right);\lambda \in \mathbb{R}\) and the point \(A\) has coordinates \(\left( 2,-3,2 \right)\).
- Exact shortest distance of \(A\) to \(l\),
- Foot of perpendicular of \(A\) to \(l\),
- Mirror image of point \(A\) in the line \(l\).
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) \(\frac{\sqrt{41}}{3}\) units (ii) \(\frac{1}{45}\left( \begin{matrix}
73 \\
-229 \\
100 \\
\end{matrix} \right)\) (iii) \(\frac{1}{45}\left( \begin{matrix}
56 \\
-323 \\
110 \\
\end{matrix} \right)\)
Need help? Join our JC Math tuition classes.
Learn more