If a line has direction ratios 2, - 1, - 2, then what are its direction cosines ?
Answers
Answer:
Step-by-step explanation:
The core concepts of three-dimensional geometry are direction cosines and direction ratios. What are direction cosines of a line that passes through the origin that makes angles with the coordinate axes? This lesson helps you understand the concepts of direction cosines and direction ratios which are nothing but numbers proportional to the direction cosines. A solved problem, in the end, will help you understand the concepts better.
Direction Cosines
In three-dimensional geometry, we have three axes: namely, the x, y, and z-axis. Let us assume a line OP passes through the origin in the three-dimensional space. Then, the line will make an angle each with the x-axis, y-axis, and z-axis respectively.
The cosines of each of these angles that the line makes with the x-axis, y-axis, and z-axis respectively are called direction cosines of the line in three-dimensional geometry. Normally, it is tradition to denote these direction cosines using the letters l, m, n respectively.
Note that these cosines can be found only once we have found the angles that the line makes with each of the axes. Also, it is interesting to note that if we reverse the direction of this line, the angles will obviously change.
Consequently, the direction cosines i.e. the cosines of these angles will also be different once the direction of the line is reversed. We will now look at a slightly different situation where our line does not pass through the origin (0,0,0).
If it will help you then plz give it a brainlist award. . . . And vote 2hh. . . ❤