What is difference between direction numbers and direction cosines for a line?
Answers
Direction ratios: Any three numbers that are proportional to the direction cosines of a line are called the direction ratios of the line. axis respectively with O as the reference, these angles are referred as the direction angles of the line and the cosine of these angles give us the direction cosines.
The difference between direction numbers and direction cosines for a line are - :
Direction ratios - :
Any three numbers that are proportional to the direction cosines of a line are called the direction ratios of the line.
Direction Cosines - :
When a directed line OP passing through the origin makes α, βand γ angles with the x, y and z
When a directed line OP passing through the origin makes α, βand γ angles with the x, y and zaxis respectively with O as the reference, these angles are referred as the direction angles of the line and the cosine of these angles give us the direction . These direction cosines are usually represented as l, m and n.
If we extend the line OP on the three dimensional Cartesian coordinate system, then to figure out the direction cosines, we need to take the supplement of the direction angles. It is pretty obvious from this statement that on reversal of the line OP in opposite direction, the direction cosines of the line also get reversed. In a situation where the given line does not pass through the origin, a line parallel to the given line passing through the origin is drawn and in doing so, the angles remain same as the angles made by the original line. Hence, we get the same direction.
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