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Q. 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 ?

JEE MainJEE Main 2020Three Dimensional Geometry

Solution:

Point on plane $R\left(-\frac{7}{3}, -\frac{4}{3}, -\frac{1}{3}\right)$
Normal vector of plane is $\frac{10}{3}\hat{i} + \frac{10}{3}\hat{j} + \frac{10}{3} \hat{k}$
Equation of require plane is $x + y + z = 1$
Hence $\left(1, -1, 1\right)$ lies on plane