 Good morning friends. I am Poojwa and today we will discuss the following question if a line makes angles 90 degree 135 degree and 45 degree with the x y and z answers respectively then find its direction cosines Now if a directed line L passing through the origin makes angles alpha beta and gamma with x y and z answers respectively then the cosines of these angles namely cos alpha cos beta and cos gamma are called direction cosines of the directed line L So this is the key idea behind a question. Let us now begin with the solution Now we are given that line makes angles 90 degree 135 degree and 45 degree with x y and z answers respectively Then by the key idea we have the direction cosines are cos 90 degree cos 135 degree and cos 45 degree Now we get the value of direction cosines as cos 90 degree is also equal to 0. So we get cos 90 degree is equal to 0 cos 135 degree is also equal to cos 90 degree plus 45 degree and this in turn is equal to minus 1 upon root 2 and Finally cos 45 degree is equal to 1 upon root 2 So we have got the direction cosines as 0 minus 1 upon root 2 and 1 upon root 2. So we write our answer as the direction cosines are 0 minus 1 upon root 2 and 1 upon root 2 This is our answer. Hope you have understood the solution. Bye and take care