The equation of a plane passing through the line of intersection of the planes x+2 y+3 z=2 and x-y+z=3 and at a distance 2 3 from the point (3,1,-1) is

Step-by-step solution

Equation of the plane passing through the intersection line of given planes is array ll & (x+2 y+3 z-2)+ (x-y+z-3)=0 or & (1+ ) x+(2- ) y+(3+ ) z+(-2-3 )=0 array Its distance from the point (3,1,-1) is 2 3 array l | 3(1+ )+1(2- )-1(3+ )+(-2-3 ) (1+ )²+(2- )²+(3+ )² |= 2 3 | -2 3 ²+4 +14 |= 2 3 3 ²+4 +14=3 ² =- 7 2 array Required equation of plane is (x+2 y+3 z-2)- 7 2 (x-y+z-3)=0 or 5 x-11 y+z=17