 Hi and welcome to the session. Let us discuss the following question. Question says, find the equation of the plane passing through A, B, C and parallel to the plane r vector dot i plus j plus k is equal to 2. First of all let us understand that if a plane passes through a point A with position vector A and normal vector is n vector, then vector equation of the plane is r vector minus a vector dot n vector is equal to 0. And Cartesian equation of the plane is a multiplied by x minus x1 plus b multiplied by y minus y1 plus c multiplied by z minus z1 is equal to 0 where a, b and c are direction ratios of vector n. This is the key idea to solve the given question. Let us now start with the solution. Now we are given plane passes through the point having coordinates a, b, c and the normal vector to the plane is parallel to r vector dot i plus j plus k is equal to 2. Now this means normal vector to the plane will be same as the normal to the given plane that is r vector dot i plus j plus k is equal to 2. So we can write therefore n vector is equal to i plus j plus k. Now position vector of the given point whose coordinates are a, b, c is represented by vector a which is equal to a i plus b j plus c k. Now from key idea we know this equation represents the vector equation of the plane. Now we know a vector is equal to a i plus b j plus c k. So here we can write r vector minus a i plus b j plus c k dot n vector n vector is equal to i plus j plus k. So here we can write i plus j plus k is equal to 0. Now this is the required vector equation of the plane. Now we will find out Cartesian equation of the plane. From key idea we know this equation represents the Cartesian equation of the plane and here a, b and c are the direction ratios of normal vector. Now clearly we can see a, b and c are equal to 1. So we can write a is equal to 1, b is equal to 1 and c is also equal to 1. And we know x1, y1, z1 are the coordinates of the given point through which plane is passing. So we can write this equation as x minus a plus y minus b plus z minus c is equal to 0. On simplifying further we get x plus y plus z is equal to a plus b plus c. So this is the required Cartesian equation of the plane and this is the required vector equation of the plane. These two equations represent our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.