 Hello and welcome to the session my name is Asha and I am going to help you with the following question which says find the ratio in which the yz plane divides the line segment form by joining the points minus 2, 4, 7 and 3, minus 5 and 8. So first let us learn the section formula which says if p with coordinates x1, y1 and z1 and q with coordinates x2, y2 and z2 are the two points and i with coordinates x, y and z divides the line segment pq in the ratio m is to n internally then x, y and z are given by mx2 plus nx1 upon m plus n, my2 plus n, y1 upon m plus n and mz2 plus nz1 upon m plus n. So with the help of this formula we are going to solve the above problem. So this is our key idea. Now let's start with the solution. Let us denote the given two points by a and b. So a is minus 2, 4, 7 and b is 3, minus 5 and 8 be the two points. Let a point p lying on the yz plane divides the line segment joining the points a and b in the ratio case to 1. Suppose this is a line which joins the point a and b and p lies on this line such that it divides the line segment ab in the ratio case to 1. Now p lies on the yz plane therefore x coordinate of 0, y and z. Now again according to the section formula the coordinates of the point which divides the line segment ab are given by the first x coordinate is given by mx2 plus nx1 upon m plus 1 and here x1, y1 and z1 are the points minus 2, 4 and 7 and here x2 is 3, y2 is minus 5 and z2 is 8. So now let us find the p and its coordinates 0, y and z. So here 0 is equal to k into x2 which is 3 plus 1 into minus 2 upon k plus 1 and we have k into minus 5 plus 1 into 4 upon k plus 1 and last we have k into 8 plus 1 into 7 upon k plus 1 which further implies that the coordinates of the point p which are 0, y and z are equal to 3k minus 2 upon k plus 1 minus 5k plus 4 upon k plus 1 and 8k plus 7 upon k plus 1. Now on comparing the coordinates we have 0 is equal to 3k minus 2 upon k plus 1 or this further implies 3k minus 2 is equal to 0 or k is equal to 2 upon 3. So here k is equal to 2 upon 3 hence the required ratio in which the yz plane divides the points a and b in the ratio k is 2, 1 is 2 upon 3 is 2, 1 or 2 is to 3. Hence our answer is the required ratio is 2 is to 3. So this completes the session hope you have understood it take care and have a good day.