 Hello and welcome to the session. In this session we discussed the following question which says find the equation of the plane passing through the point that coordinates minus 1, 3, 2 and perpendicular to each of the planes x plus 2y plus 3z equal to 5 and 3x plus 3y plus z equal to 0. Before we move on to the solution, let's recall the equation of the plane passing through a point which coordinates x1, y1, z1 is given by a into x minus x1 plus b into y minus y1 plus c into z minus z1 equal to 0 where a, b and c are the direction ratios of the normal to the plane. Next let's see what is the condition of the two planes to be perpendicular to each other. Consider two planes a1x plus b1y plus c1z plus d1 equal to 0 and a2x plus b2y plus c2z plus d2 equal to 0 then these two planes are perpendicular a1a2 plus b1b2 plus c1c2 is equal to 0. This is the key idea that we use for this question. Let's proceed with the solution now. We are given a point, say point a with coordinates minus 1, 3, 2. Now the equation of the plane passing through the point a with coordinates minus 1, 3, 2 is a into x minus minus 1 that is the x coordinate of point a plus b into y minus y coordinate of point a that is 3 plus c into z minus z coordinate of point a that is 2 is equal to 0. Now we get a into x plus 1 plus b into y minus 3 plus c into z minus 2 is equal to 0. Let this be equation 1. Now the other two planes given to us are x plus 2y plus 3z equal to 5. Let this be equation 2 and 3x plus 3y plus z is equal to 0. Let this be equation 3. It's given that plane 1 is perpendicular to plane 2. Therefore, we have into 1 that is a plus b into 2 that is 2b plus c into 3 that is 3c is equal to 0 using the condition given in the key idea. We take this as equation 4. Now next we have plane 1 is perpendicular to plane 3. Therefore, we have a into 3 that is 3a plus 3 into b 3b plus c into 1 that is c is equal to 0 using the condition given in the key idea for the two planes to be perpendicular. So let this be equation 5. So now eliminating a, b and c from equations 1, 4 we get determinant with elements in the first row as x plus 1, y minus 3 and z minus 2. In the second row the elements are 1, 2 and 3. In the third row the elements are 3, 3 and 1 and this determinant is equal to 0. So this gives us x plus 1 into 2 into 1 that is 2 minus 3 into 3 that is 9 minus y minus 3 just multiplied by 1 into 1 that is 1 minus 3 into 3 that is 9 plus z minus 2 into 1 into 3 that is 3 minus 3 into 2 which is 6 is equal to 0. So this means we have minus 7 into x plus 1 plus 8 into y minus 3 minus 3 into z minus 2 is equal to 0. That is minus 7x minus 7 plus 8y minus 24 minus 3z plus 6 is equal to 0. This gives us minus 7x plus 8y minus 3z minus 25 is equal to 0. Hence we have 7x minus 8y plus 3z plus 25 is equal to 0. Hence the required equation of the plane is 7x minus 8y plus 3z plus 25 is equal to 0. This is our final answer. So this completes the session. Hope you have understood the solution of this question.