 Hi friends, I am poor wine today. We will discuss the following question in the following find the distance of the given point from the corresponding given plane the point is 000 and the plane is 3x minus 4y plus 12z is equal to 3 now let the equation of the plane be ax plus by Plus Cz is equal to D and let the given point be x1 y1 z1 then the distance of this point from the plane is given by mod of ax1 plus by 1 plus Cz1 minus D upon under root of a square plus b square plus C square So this is the key idea behind our question Let us begin with the solution now Now we are given the equation of the plane as 3x minus 4y plus 12z is equal to 3 and the given point is 000 now comparing the equation of the plane with ax plus by Plus Cz is equal to D. We see that Here a is equal to 3 B is equal to minus 4 C is equal to 12 and D is equal to 3 Also the point x1 y1 z1 is 000 Now by key idea. We know that the distance of the point x1 y1 z1 from the plane ax plus by plus Cz is Equal to D is given by mod of ax1 plus by 1 plus Cz1 minus D upon under root of a square plus b square plus c square So here we get required distance is Equal to mod of ax1 plus by 1 plus Cz1 Minus D upon under root of a square plus b square plus C square This is equal to mod of ax1 is 3 into 0 Plus by 1 is minus 4 into 0 Plus Cz1 is 12 into 0 Minus D is equal to minus 3 Upon under root of a square that is 3 square Plus b square that is minus 4 whole square Plus c square that is 12 square This is equal to mod of Minus 3 upon under root of 9 plus 16 plus 144 this is equal to mod of minus 3 upon under root of 169 which is further equal to 3 upon under root of 169 and This is equal to 3 upon 13 So we have got our answer as 3 upon 13. Hope you have understood the solution. Bye and take care