 Good morning friends I am Purva and today we will work out the following question. In the following find the distance of the given point from the corresponding given plane. The point is minus x 0 0 and the plane is 2x minus 3y plus xz minus 2 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 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 2x minus 3y plus 6z minus 2 is equal to 0 or we can write this as 2x minus 3y plus 6z is equal to 2 and the given point is minus 6 0 0. Now comparing this equation of the plane with ax plus by plus cz is equal to d we see that a is equal to 2 b is equal to minus 3 c is equal to 6 and d is equal to 2. Also we have point x1 y1 z1 is minus 6 0 0. 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 which is equal to 2 into minus 6 plus by 1 that is minus 3 into 0 plus cz1 that is 6 into 0 minus d that is minus 2 upon under root of a square that is 2 square plus b square that is minus 3 whole square plus c square that is 6 square this is equal to mod of 2 into minus 6 is minus 12 minus 3 into 0 is 0 6 into 0 is 0 minus 2 upon under root of 2 square is equal to 4 plus minus 3 whole square is equal to 9 plus 6 square is equal to 36 this is equal to mod of minus 14 upon under root 49 which is equal to 14 upon under root 49 this is equal to 14 upon 7 and this is further equal to 2 so we have got the required distance as 2 this is our answer hope you have understood the solution bye and take care