If n =2 i -3 j +4 k , m = i - j , l =2 i - j + k , then the Cartesian equation of the plane passing through the line of intersection of two planes r . n =1 and r . m =-4 and perpendicular to the plane r l =-8 is

Step-by-step solution

Plane passing through the line of intersection of planes r n =1 and r m =-4 r ( n + m )=1-4 ( where is a scalar quantities) This plane is to the plane r 1 =-8 So, gathered ( n + m ) l =0 n 1 + m 1 =0 gathered aligned (2 i -3 j +4 k ) (2 i - j & + k ) & + ( i - j ) (2 i - j + k )=0 (4+3+4)+ (2+1) & =0 & = -11 3 . aligned So, required plane is, gathered r [2 i -3 j +4 k -11 3 ( i - j ) ]=1-4 ( -11 3 ) r ( -5 i 3 + 2 j 3 +4 k )= 47 3 (x i +y j +z k ) (-5 i +2 j +12 k )=47 [ r =x i +y j +z k ] -5 x+2 y+12 z=47 5 x-2 y-