Correct option is (A) a/8 = b/5 = c/-4
Let equation of rotated plane be :
(2x + 3y + z + 20) + λ (x – 3y + 5z – 8) = 0
(2 + λ )x + (3 – 3λ )y + (1 + 5l)z + 20 – 8λ = 0
Above plane is perpendicular to 2x + 3y + z + 20 = 0
So, (2 + λ ).2 + (3 – 3λ ).3 + (1 + 5λ).1 = 0
⇒ λ = 7
⇒ Equation of rotated plane : x – 2y + 4z – 4 = 0
Mirror image of A(2, -1/2, 2) in rotated plane is B(a, b, c)
Equation of AB : \(\frac{x-2}1=\frac{(y+1)/2}{-2}=\frac{z-2}4=k\)
Let coordinate of B be (2 + k/2, -1/2 - k, 2 + 2k) which will lie on the plane x - 2y + 4z - 4 = 0
Hence k = -2/3
Therefore B is (4/3, 5/6, -2/3) = (8/6, 5/6, -4/6)
So, a/8, b/5 = c/-4