what is the actual use of direction cosines... and wht happens actually when we consider direction cosines..please answer in detail..!
well why do we only consider direction cosines... why not direction sines,tans..??
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We are going to describe the direction of a line through the origin. I need to tell you how, starting at the origin, you walk so many steps parallel to the x-axis, then so many steps parallel to the y-axis, then so many steps parallel to the z-axis, to arrive at a point on the line distant exactly one from the origin. If I stood at that point and dropped a perpendicular on each of the axes in turn, the perpendicular would hit the axis at the point with coordinates (cosΘx,0,0), (0,cosΘy,0),(0,0,cosΘz). I need to say that Θx is the angle between the line and the x-axis, and similarly for the other angles.
If you need to walk on a line which doesn't go through the origin, then the same exercise is applied by walking from any point on the line, say (a,b,c), and the answers change to (a+cosΘx,b,c),(a,b+cosΘy,c),(a,b,c+cosΘz) which is seen by drawing a set of axes through (a,b,c) rather than the origin.