Physicists are investigating the reflective property of a particular reflective surface. The diagram

Question

Physicists are investigating the reflective property of a particular reflective surface. The diagram below shows the set-up of a particular experiment, where a laser emitting device was placed at the point with coordinates $(1, 2, 3)$. A laser beam was emitted in the direction parallel to $\mathbf{i} + \mathbf{k}$. The path of the emitted laser beam and its reflected path make the same angle $\theta$ with the reflective surface. The plane containing these two paths is perpendicular to the reflective surface.

Write down the vector equation of the path of the emitted laser beam.[1]

Diagram of laser reflection

It is known that the reflective surface has equation $x + y + z = 4$.

Find $\theta$.[3]
Show that the laser beam meets the reflective surface at the point $(0, 2, 2)$.[3]
Find the vector equation of the path of the reflected laser beam.[5]

Accepted Answer

Emitted path: $\mathbf r=\begin{pmatrix}1\2\3\end{pmatrix}+\lambda\begin{pmatrix}1\0\1\end{pmatrix}$ (i) $54.7^\circ$ (ii) $(0,2,2)$ (iii) $\mathbf r=\begin{pmatrix}0\2\2\end{pmatrix}+\mu\begin{pmatrix}1\4\1\end{pmatrix}$, $\mu\ge0$

2017 VJC P1 Q11

2017 VJC P1 Q11

Video Solution:

Solution:

Solution locked