 Hello and welcome to the session. My name is Asha and I am going to help you with the following question that says, using friction formula show that the points A, B and C are collinear. That is we have to show that the points A, B and C lie on the same line. So let's start with the solution. Now let P with coordinates X, Y and Z divides the joint of points A and B in the ratio case to 1. So here the line segment AB is divided by the point P in the ratio case to 1 and the coordinates of the point P or X, Y and Z which by the section formula we know that are given by, X is given by K into minus 1 plus 1 into 2 upon K plus 1, Y is given by K into 2 plus 1 into minus 3 upon K plus 1 and the Z coordinates is given by K into 1 plus 1 into 4 upon K plus 1 which further implies that X, Y and Z are equal to minus K plus 2 upon K plus 1, 2K minus 3 upon K plus 1 and K plus 4 upon K plus 1. Now comparing we have X is equal to minus K plus 2 upon K plus 1, Y is equal to 2K minus 3 upon K plus 1 and Z is equal to K plus 4 upon K plus 1. Now let us see if for some value of K the point P coincides with the point C with coordinates 0, 1 upon 3 and 2 to be 0. This implies minus K plus 2 upon K plus 1 is equal to 0 or K is equal to 2. Now let us put K is equal to 2 in the Y coordinate of P and Z coordinate of P. The Y coordinate of P is 2K minus 3 upon K plus 1 on substituting K is equal to 2, we have 2 into 2 minus 3 upon 2 plus 1 which gives 1 upon 3 and now let us find the Z coordinate of P is K plus 4 upon K plus 1. So we have 2 plus 4 upon 2 plus 1 which is equal to 6 upon 3 which is further equal to 2. Thus the X, Y and Z coordinate that is P X, Y and Z is equal to 0, 1 upon 3 and 2 which coincides with the point C with the same coordinate 0, 1 upon 3 and 2 and since the point P lies on the line segment AB hence in other words we can say that C 0, 1 upon 3 and 2 divides AB in the ratio K is to 1 and K is 2 so 2 is to 1 and therefore C lies on the line segment AB and thus thus further implies that AB and C points are collinear. So this completes the session, hope you have understood it well, take care and have a good day.