JEE Mains · Maths · STD 12 - 11. three dimension geometry
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 ?
- A \((-1, -1, -1)\)
- B \((-1, -1, 1)\)
- C \((1, 1, 1)\)
- D \((1,- 1, 1)\)
Answer & Solution
Correct Answer
(D) \((1,- 1, 1)\)
Step-by-step Solution
Detailed explanation
Point on plane \(\mathrm{R}\left(\frac{-2}{3}, \frac{1}{3}, \frac{4}{3}\right)\) Normal vector of plane is \(\frac{10}{3} \hat{\mathrm{i}}+\frac{10}{3} \hat{\mathrm{j}}+\frac{10}{3} \hat{\mathrm{k}}\) Equation of require plane is \(x+y+z=1\) Hence \((1,-1,1)\) lies on plane
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