 Hello and welcome to the session. In this session we discussed the following question which says, a plane meets the coordinate axis at A, B, C such that the center point of triangle A, B, C is 2, 6 minus 8. Find the equation of the plane. Let's see the solution now. We have to find the equation of the plane which meets the coordinate axis at the points A, B and C and it's given that the centroid of triangle A, B, C has coordinates 2, 6 minus 8. Now we know that the equation of a plane which cuts off, intercepts A, B, C from the x-axis, y-axis and z-axis respectively is given as x upon A plus y upon B plus z upon C equal to 1. Let this be equation 1. So this is the general equation of the plane. So we have that the plane cuts, intercepts A from the x-axis. So the plane meets the coordinate axis say the x-axis at point A which has coordinates A, 0, 0. It meets the coordinate axis y-axis at point B which coordinates 0, B, 0. Since the plane cuts off intercept B from the y-axis and the point C where the plane meets the z-axis would be 0, 0, C since C is the intercept which the plane cuts from the z-axis. We take let alpha, beta, gamma be the coordinates of the centroid of triangle ABC. So this would mean that alpha is equal to x-coordinate of A which is A plus the x-coordinate of B which is 0 plus the x-coordinate of C which is 0 upon 3 and this is equal to A upon 3, beta is equal to the y-coordinate of A which is 0 plus the y-coordinate of B which is B plus the y-coordinate of C which is 0 upon 3 and this is equal to B upon 3. Then we have gamma is equal to the z-coordinate of A which is 0 plus the z-coordinate of B which is 0 plus the z-coordinate of C which is C upon 3 and this is equal to C upon 3. And we know that the centroid of triangle ABC is given as 2, 6 minus 8. Therefore we can say that alpha is equal to 2, beta is equal to 6 and gamma is equal to minus 8. Now as we know that alpha is equal to A upon 3, so we have A upon 3 is equal to 2 which means that A is equal to 6, then beta is equal to 6 means B upon 3 is equal to 6 which gives us B equal to 18, then gamma is equal to minus 8 means C upon 3 equal to minus 8 which gives us C equal to minus 24. So we have got the values for A, B and C. Now substituting the values of A, B and C in equation 1 we get. Now this is the equation 1, so I am putting the values for A, B and C we would get x upon 6 plus y upon 18 plus z upon minus 24 is equal to 1 that is x upon 6 plus y upon 18 minus z upon 24 is equal to 1. So further we get 72 in the denominator by taking the LCM of the denominator of these fractions. So in the numerator we get 12x plus 4y minus 3z is equal to 1 or you can say we have 12x plus 4y minus 3z equal to 72. So this is the required equation of the plane. So this is our final answer, this completes the session, hope you have understood the solution of this question.