The equation of a plane containing the point (1,-1,2) and perpendicular to the planes 2 x+3 y-2 z=5 and x+2 y-3 z=8 is

Step-by-step solution

(A) The equation of a plane passing through (1,-1,2) is a(x-1)+b(y+1)+c(z-2)=0 If is perpendicular to the planes 2 x+3 y-2 z=5 and x+2 y-3 z=8 . 2 a +3 ~b -2 c =0 and a +2 ~b -3 c =0 Solving the above equation, we get, array l a | array cc 3 & -2 2 & -3 array | = -b | array ll 2 & -2 1 & -3 array | = c | array ll 2 & 3 1 & 2 array | a -5 = b 4 = c 1 array Substituting a =-5, ~b =4 and c =1 , we get, -5 x+4 y+z=-7 5 x-4 y-z=7 Required equation can be written as r (5 i -4 j - k )=7