 Hello and welcome to the session. In this session, we will discuss a question which says that find the equation of the plane which passes through the point P whose coordinates are 4, 2, 3 and is perpendicular to the planes 2x plus 2y minus there minus 5 is equal to 0 and minus 3x plus y plus 2z plus 3 is equal to 0. Now before starting the solution of this question, we should know some results. First is the equation of a plane passing through the point x1, y1, z1 is given by a into x minus x1 the whole plus b into y minus y1 the whole plus c into z minus z1 the whole is equal to 0 where a, b and p are the constants and second is the planes a1x plus b1y plus c1z plus b1 is equal to 0 and a2x plus b2y plus c2z plus d2 is equal to 0 are perpendicular a1 into a2 plus b1 into b2 plus c1 into c2 is equal to 0. Now these results will work out as a key idea for solving out this question and now we will start with the solution. Now we have to find the equation of the plane which passes through the point whose coordinates are given to us and is perpendicular to the given planes. So given that the plane passes through the point p whose coordinates are 4, 2, 3. Now using this result which is given in the key idea, the equation of the plane passing through the point p whose coordinates are 4, 2, 3 is given by a into x minus x1 the whole that will be x minus 4 the whole plus b into y minus y1 the whole that will be b into y minus 2 the whole plus c into z minus z1 that will be c into z minus 3 the whole is equal to 0 which further implies ax minus 4a plus by minus 2b plus cz minus 3c is equal to 0 which implies ax plus by plus cz minus 4a minus 2b minus 3c is equal to 0. Now let this be equation a and this be equation number 1 now given that the plane which is given by equation number 1 is perpendicular to the plane whose equation is given as 2x plus 2y minus z minus 5 is equal to 0 so using the condition of perpendicularity we have if these two planes are perpendicular to each other therefore a1 into a2 that is 2a plus b1 into b2 that is plus 2b plus c1 into c2 that is c into minus 1 that will be minus c is equal to 0. Also the plane which is given by equation number 1 is perpendicular to the plane minus 3x plus y plus 2z plus 3 is equal to 0 therefore by using the condition of perpendicularity it will be also a1 into a2 that is minus 3a plus b1 into b2 that is plus b plus c1 into c2 that is plus 2c is equal to 0. Now let this be equation number 2 and this be equation number 3 now solving equations 2 and 3 by the method of cross multiplication a over 2 into 2 that is 4 minus minus 1 into 1 that is minus 1 is equal to b over minus 3 into minus 1 that is 3 minus 2 into 2 that is 4 is equal to c over 2 into 1 that is 2 minus 2 into minus 3 that is minus 6 and let this be equal to k which is the constant k. Now this implies a over 5 is equal to b over minus 1 is equal to c over 8 is equal to k which implies a is equal to 5k b is equal to minus k and c is equal to 8k. Now this is the equation a now putting the values of a b and c in equation a we get 5k into x minus 4 the whole minus k into y minus 2 the whole plus 8k into z minus 3 the whole is equal to 0 which implies now dividing throughout by k and solving this will be 5x minus 20 minus y plus 2 plus 8z minus 24 is equal to 0 which implies 5x minus y plus 8z minus 42 is equal to 0 which is the required equation of the plane. So this is the solution of the given question and that's what for this session hope you all have enjoyed the session.