 Good morning friends. I am Purva and 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 3 minus 2 1 and the plane is 2x minus y plus 2z plus 3 is equal to 0. Now, let the equation of the plane be Ax plus By plus Cz is equal to D and the given point be x1, y1, z1. Then the distance of this point from the plane is given by mod of Ax1 plus By1 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 2x minus y plus 2z plus 3 is equal to 0 or we can write this as 2x minus y plus 2z is equal to minus 3 and the given point is 3 minus 2 1. 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 2, B is equal to minus 1, C is equal to 2 and D is equal to minus 3. Also the point x1, y1, z1 is 3 minus 2 1. 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 By1 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 By1 plus Cz1 minus D upon under root of A square plus B square plus C square. This is equal to mod of now Ax1 is equal to 2 into 3 plus By1 is equal to minus 1 into minus 2 plus Cz1 is equal to 2 into 1 minus D that is minus of minus 3 which is equal to plus 3 upon under root of A square that is 2 square plus B square that is minus 1 whole square plus C square that is 2 square. This is equal to mod of 2 into 3 is 6 minus 1 into minus 2 is plus 2 2 into 1 is 2 plus 3 upon under root of 2 square is equal to 4 minus 1 whole square is equal to 1 plus 2 square is equal to 4. This is equal to mod of 13 upon under root 9 which is equal to 13 upon under root 9 and this is equal to 13 upon 3. So we have got our answer as 13 upon 3. Hope you have understood the solution. Bye and take care.