A plane which is perpendicular to two planes 2 x-2 y+z=0 and x-y+2 z=4 , passes through (1,2,1) . The distance of the plane from the point (2,3,4) is

Step-by-step solution

- A plane perpendicular to two given planes passes through (1,2,1) . The distance of the plane from the point (2,3,4) . 1. Let the plane equation passing through (1,2,1) be: a(x-1)+b(y-2)+c(z-1)=0 2. The plane is perpendicular to the two given planes: - 2 x-2 y+z=0 - x-y+2 z=4 Thus, the normal vector of the required plane is perpendicular to the normal vectors of these planes. 3. Solve the normal vectors using the cross-product method: - Normal to plane 1: n₁ =(2,-2,1) - Normal to plane 2: n₂ =(1,-1,2) - Cross prod