 Hello and welcome to the session my name is Mansi and I am going to help you with the following question. The question says find the equation of the set of points which are equidistant from the points 1, 2, 3 and 3, 2 minus 1. Before starting with the solution let us see the key idea behind the question that is if a point p say x1, y1, z1 and the point q, x2, y2, z2 are two points then the distance between them with pq is given by square root of x2 minus x1 the whole square, thus y2 minus y1 the whole square, the z2 minus z1 the whole square. So let us start with the solution to this question now. Here the two given points are point a that is 1, 2, 3 and the point b that is 3, 2, minus 1 let p a point with coordinates x, y, z be the point equidistant from the points a that is 1, 2, 3 and b that is 3, 2, minus 1. Now distance between the point p and a is given by p a that is equal to square root of x minus 1 the whole square plus y minus 2 the whole square plus z minus 3 the whole square also distance between the point p and b is given by pb that is equal to square root of x minus 3 the whole square plus y minus 2 the whole square plus z plus 1 the whole square. Now it is given to us that the point p is equidistant from a and b that means the distance p a is equal to pb. So we can say that this is equal to this that is square root of x minus 1 the whole square plus y minus 2 the whole square plus z minus 3 the whole square is equal to the square root of x minus 3 the whole square plus y minus 2 the whole square plus z plus 1 the whole square. Now squaring both sides we get x minus 1 the whole square plus y minus 2 the whole square plus z minus 3 the whole square is equal to x minus overall square plus y minus 2 the whole square plus z plus 1 the whole square. Now on cancelling y minus 2 the whole square from both the sides we get x minus 1 the whole square, plus z minus 3 the whole square is equal to x minus 3 the whole square plus z plus 1 the whole square. Now let us open the brackets on both the sides. We get x squared minus 2x plus 1 plus z squared minus 6z plus 9 is equal to x squared minus 6x plus 9 plus z squared plus 2z plus 1. Now we see that x squared gets cancelled with x squared from both the sides. Also z squared gets cancelled with z squared. We have minus 2x minus 6z plus 9 plus 1 is 10 is equal to minus 6x plus 2z plus 1 plus 9 is 10. Again 10 gets cancelled with 10 from both the sides. We have minus 2x plus 6x minus 6z minus 2z is equal to 0. This implies now minus 2x plus 6x is 4x minus 6z minus 2z is minus 8z is equal to 0. Now taking 4 common from both the terms we have 4 into zx minus 2z equal to 0. Since 4 is not equal to 0 this implies x minus 2z is equal to 0 which is the required equation. So our answer to the question is that equation of the set of points which are equidistant from the points 1, 2, 3 and 3, 2 minus 1 is x minus 2z equal to 0. So this is our answer to the question. I hope that you understood the question and enjoyed the session. Have a good day.