 Now before starting the solution of this question we should know a result and that is, let the equations of the two planes be a1x plus b1y plus c1z plus d1 is equal to 0 and a2x plus b2y plus c2z plus d2 is equal to 0. Now let that is the point p whose coordinates are x, y, z, the n point on n1 of the planes by setting the angles between the planes which are given by equation number 1 and 2. Then the perpendicular from the point p x, y, z must be numerically equal. The equations of the two sectors between the planes which are given by equation number 1 and 2, a1x plus b1y plus c1z plus d1, whole upon square root of a1 square plus b1 square plus c1 square is equal to plus minus a2x plus b2y plus c2z plus d2 whole upon square root of a2 square plus b2 square plus c2 square. The second equation of the bisector is the bisector of the acute angle between the planes and other is the bisector of the obtuse angle between the planes. Now this result will work out as a key idea for solving out this question. And now we will start with the solution the equations of the planes are given to us and we have to find the equations of the bisector planes of the angles between the given planes. So given the equations z minus 4 is equal to 0, z minus 7 is equal to 0. Now let this be equation number 1 and this be equation number 2. Now using the result which is given in the key idea whose coordinates are x, y, z be any point on the bisector planes then the perpendicular x, y, z must be numerically equal. The equations between which are given by equation number 1 so the equations of the bisectors are that is 2x plus b1y that is 2y and z that is plus z plus d that is minus 4 square root of a1 square that is 2 square which is 4 plus v1 square that is 2 square which is 4 plus c1 square that is 1 square which is 1 is equal to plus minus a2x that is 3x v2y that is 2y plus c2z that is plus 6z minus 7 square root of a2 square that is 3 square which is 9 plus v2 square that is 2 square which is 4 is 36. Now this implies that z minus 4 is equal to root 9 which is 3 is equal to root 49 which is equal to 7 which are the equations. Let it be equation a we get that is here we will consider only the positive sign so this will become 2x plus 2y plus z minus 4 whole upon 3 is equal to plus 3x plus 2y plus 6z minus 7 whole upon 7. And this implies that minus 28 is equal to 9x plus 6y plus 18z minus 21 which further implies minus 9x plus 14y minus 6y plus 7z minus 18z minus 28 plus 21 is equal to 0. Which further implies 5x plus 8y minus 11z minus 7 is equal to 0. Equation of one of the pi sector planes negative sign in a we get z minus 4 whole upon 3 is equal to minus z minus 7 the whole 14y plus 7z minus 28 is equal to minus 9x minus 6 14x plus 9x 18z minus 21 is equal to 0. Which further implies 2y plus 25z minus 49 is equal to 0. Hence the equations 8y minus 11z minus 7 is equal to 0. 21 plus 25z minus 49 is equal to 0. So this was the solution of the given question and that's all for this session. Hope you all have enjoyed the session.