 Hi and welcome to the session I am Shashi and I am going to help you with the following question. Question says find the equation of the plane passing through the point minus 1, 3, 2 and perpendicular to each of the planes x plus 2y plus 3z is equal to 5 and 3x plus 3y plus z is equal to 0. First of all let us understand that equation of a plane perpendicular to a given line with direction ratios a, v, c and passing through a point x1, y1, z1 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. This is the key idea to solve the given question. Let us now start with the solution. The equation of plane passing through the point minus 1, 3, 2 is given by a multiplied by x plus 1 plus b multiplied by y minus 3 plus c multiplied by z minus 2 is equal to 0. Clearly we can see to write this equation we have used key idea. Let us name this equation as equation 1. Now we know this equation of the plane or we can say this plane is perpendicular to the plane given by the equations x plus 2y plus 3z is equal to 5 and 3x plus 3y plus z is equal to 0. This is given in the question that this plane is perpendicular to both of these planes. Now we can write applying condition of perpendicularity to the plane given in equation 1 with the given planes we get a plus 2b plus 3c is equal to 0. Clearly we can see direction ratios in this plane are a, b, c and direction ratios in this plane are 1, 2, 3. a multiplied by 1 plus b multiplied by 2 plus c multiplied by 3 must be equal to 0 as both of these planes are perpendicular to each other. Similarly we will multiply direction ratios of these two planes and we get 3a plus 3b plus c is equal to 0. Now we can write 3a plus 3b plus c is equal to 0. Let us name this equation as 2 and this equation as 3. Now we will solve these two equations to find the value of a, b and c. First of all we will multiply both the sides of this equation by 3 and then we will subtract equation 3 from it and we get 3b plus 8c is equal to 0 or we can write c is equal to minus 3b upon 8. Now we will substitute this value of c in equation 2 and we get a is equal to minus 7 upon 8b. Now substituting values of a and c in equation 1 we get minus 7 upon 8b multiplied by x plus 1 plus b multiplied by y minus 3 plus minus 3 upon 8b multiplied by z minus 2 is equal to 0. Now dividing both the sides of this equation by b we get minus 7 upon 8 multiplied by x plus 1 plus y minus 3 minus 3 upon 8 multiplied by z minus 2 is equal to 0. Now this further implies minus 7x minus 7 plus 8y minus 24 minus 3z plus 6 is equal to 0. Solving the brackets and adding the terms by taking their LCM we get this equation. Now solving the like terms we get 7x minus 8y plus 3z plus 25 is equal to 0. So this is the required equation of the plane. This completes the session hope you understood the solution take care and have a nice day.