Question:
The mirror image of the point $(1,2,3)$ in a plane is
$\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right)$. Which of the following points lies on this plane?
Correct Option: , 2
Solution:
$\vec{n}=\frac{-7}{3}-1, \frac{-4}{3}-2, \frac{-1}{3}-3$
$\vec{n}=\frac{10}{3}, \frac{10}{3}, \frac{10}{3}$
$D . r$ of normal to the plane
$(1,1,1)$
Midpoint of $P$ and $Q$ is
$\left(\frac{-2}{3}, \frac{1}{3}, \frac{4}{3}\right)$
$\therefore \quad$ Equation of required
$Q\left(\frac{-7}{3}, \frac{-4}{3}, \frac{-1}{2}\right)$
plane $Q$
$\vec{r} \cdot \vec{n}=\vec{a} \cdot \vec{n}$
$\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=\frac{-2}{3}+\frac{1}{3}+\frac{4}{3}$
$\therefore$ Equation of plane is $x+y+z=1$