 Good morning friends I am Purva and today we will work out the following question, find the direction cosines of a line which makes equal angles with the coordinate axis. Now if a directed line L passing through the origin makes angles alpha, beta and gamma with x, y and z axis respectively then cosines of these angles namely cos alpha cos beta and cos gamma are called direction cosines of the directed line L. Now let the direction cosines be L, M and N, then the relation between them is given by L square plus M square plus N square is equal to 1 and this is the key idea behind our question. Let us now begin with the solution, now we are given that line makes equal angles with x, y and z axis respectively as the direction cosines are also equal to one another. Now from key idea we know that L, M and N are the direction cosines so we get this implies L is equal to M is equal to N. Now from key idea we also know that L square plus M square plus N square is equal to 1. Now putting L is equal to M is equal to N we get L square plus L square plus L square is equal to 1 which implies 3 L square is equal to 1 which further implies L square is equal to 1 upon 3 and this implies L is equal to plus minus 1 upon root 3. Now since we are given that the value of all direction cosines is the same that is L is equal to M is equal to N therefore we get the direction cosines are plus minus 1 upon root 3 comma plus minus 1 upon root 3 comma plus minus 1 upon root 3 this is our answer. Hope you have understood the solution, bye and take care.