Question

What does direction ratio actually mean???? Because the definition saying that 3 numbers proportional to the direction cosines of a line is called a direction ratio is not So imaginable ...

Answer 1

Direction ratios provide a convenient way of specifying the direction of a line in three dimensional space.
Direction cosines are the cosines of the angles between a line and the coordinate axes.

Direction Ratios and Cosines in Three Dimensions
The concepts of direction ratio and direction cosines extend naturally to three dimensions.
Given a vector r = ai + bj + ck its direction ratios are a : b : c.
This means that to move in the direction of the vector we must must move a units in the x direction and b units in the y direction for every c units in the z direction.
The direction cosines are the cosines of the angles between the vector and each of the axes.
It is conventional to label direction cosines as , m and n and they are given by
l=cos α = a /(√(a² + b² + c²)), m = cos β = b/( √(a² + b² + c²)) , n = cos γ = a/ (√(a² + b² + c²))
In general we have the following result:
For any vector r = ai + bj + ck its direction ratios are a : b : c.
Its direction cosines are = a /(√(a² + b² + c²)) , m = b /(√(a² + b² + c²)) , n = c /(√(a² + b² + c² ))
where l² + m² + n² = 1