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?
Select the correct option:
A
(–1, –1, –1)
B
(1, 1, 1)
C
(–1, –1, 1)
D
(1, –1, 1)
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Let A(1, 2, 3), B (−7/3, −4/3, −1/3)
Mid-point of AB = (−2, −1, 4/3)
Let equation of plane is
a(x + 2/3) + b(y − 1/3) + c(z − 4/3) = 0 …(i)
dr’s of AB = 10/3, 10/3, 10/3
∴ Equation of plane is
x + 2/3 + y − 1/3 + z − 4/3 = 0
⇒ x + y + z = 1
∴ (1, −1, +1) lies on the plane
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