 Good morning friends. I am Purva and today we will work out the following question show that the points 2, 3, 4 minus 1, minus 2, 1 and 5, 8, 7 are collinear. If the direction ratios of two lines are proportionate then they are parallel to one another and if there is a common point between these two parallel lines then this means that the points are collinear too. Now the direction ratios of line joining two points x1, y1, z1 and x2, y2, z2 are x2 minus x1, y2 minus y1, z2 minus z1. So this is the key idea behind the question. Let us begin with the solution now. Now we are given the three points are 2, 3, 4, minus 1, minus 2, 1 and 5, 8, 7. So let A be 2, 3, 4, B be minus 1, minus 2, 1 and C be 5, 8, 7. The direction ratios of line joining A and B are. Now by key idea we know that the direction ratios of line joining two points x1, y1, z1 and x2, y2, z2 are x2 minus x1, y2 minus y1, z2 minus z1. So the direction ratios of line joining A and B are minus 1, minus 2, minus 2, minus 3, 1 minus 4. That is we have minus 3, minus 5, minus 3. We mark this as 1. Now the direction ratios of line joining B and C are 5 plus 1, 8 plus 2, 7 minus 1. That is we have 6, 10, 6 taking minus 2 common we get or minus 3, minus 5, minus 3. We mark this as 2. From 1 and 2 we can see that the direction ratios of line AB and BC are proportional. Hence we have AB is parallel to BC but point B is common to both AB and BC. Therefore AB and C are collinear points. The points 2, 3, 4, minus 1, minus 2, 1 and 5, 8, 7 are collinear. This is our answer. Hope you have understood the solution. Bye and take care.