Let the plane 2x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x - 3y + 5z = 8. If the mirror image of the point 
in the rotated plane is B(a, b, c), then :
Text Solution
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Let equation of rotated plane be :
(2x + 3y + z + 20) + 
(x - 3y + 5z - 8) = 0
(2 + 
)x + (3 - 3 
)y + (1 + 5 
)z + 20-8 
=0
Above plane is perpendicular to 2x + 3y + z + 20 = 0
So, (2 + 
).2 + (3 - 3 
).3 + (1 + 5 
). 1 = 0 
= 7
Equation of rotated plane :x-2y + 4z-4 = 0
Mirror image of 
in rotated plane is
B(a, b, c)
Equation of 
Let coordinate of B be 
midpoint of AB is 
which
will lie on the plane x-2y + 4z-4 = 0
Hence 
Therefore B is 
So, 
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