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Direction cosines of a line are
- a)The tangents of the angles made by the line with the negative directions of the coordinate axes.
- b)The sines of the angles made by the line with the positive directions of the coordinate axes.
- c)The cotangents of the angles made by the line with the negative directions of the coordinate axes.
- d)The cosines of the angles made by the line with the positive directions of the coordinate axes.
Correct answer is option 'D'. Can you explain this answer?
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Direction cosines of a line area)The tangents of the angles made by th...
Direction cosines of a line are the cosines of the angles made by the line with the positive direction of the coordinate axis.i.e. x- axis , y-axis and z – axis respectively.
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Direction cosines of a line area)The tangents of the angles made by th...
Understanding Direction Cosines
Direction cosines are essential for defining the orientation of a line in three-dimensional space. They represent the cosines of the angles formed between the line and the positive axes of the coordinate system.
Definition of Direction Cosines
- Direction cosines are denoted by l, m, and n.
- These correspond to the angles θx, θy, and θz made with the positive x, y, and z axes, respectively.
- Mathematically, they can be expressed as:
- l = cos(θx)
- m = cos(θy)
- n = cos(θz)
Why Option D is Correct
- The correct answer states that direction cosines are the cosines of the angles made by the line with the positive directions of the coordinate axes.
- This means that when you measure the angle between the line and each of the positive axes, the direction cosines provide a direct representation of how "aligned" the line is with respect to each axis.
- For instance, if a line makes an angle of 30 degrees with the x-axis, the direction cosine (l) would be cos(30°), which equals √3/2.
Clarification on Other Options
- Option A talks about tangents, which do not represent direction cosines.
- Option B mentions sines, which represent direction sines, not cosines.
- Option C refers to cotangents, which again do not define direction cosines.
Conclusion
In summary, the direction cosines are indeed the cosines of the angles made with the positive directions of the coordinate axes, confirming that option D is the accurate choice. Understanding this concept is crucial for solving various problems in geometry and physics, especially in the context of JEE.
Direction cosines are essential for defining the orientation of a line in three-dimensional space. They represent the cosines of the angles formed between the line and the positive axes of the coordinate system.
Definition of Direction Cosines
- Direction cosines are denoted by l, m, and n.
- These correspond to the angles θx, θy, and θz made with the positive x, y, and z axes, respectively.
- Mathematically, they can be expressed as:
- l = cos(θx)
- m = cos(θy)
- n = cos(θz)
Why Option D is Correct
- The correct answer states that direction cosines are the cosines of the angles made by the line with the positive directions of the coordinate axes.
- This means that when you measure the angle between the line and each of the positive axes, the direction cosines provide a direct representation of how "aligned" the line is with respect to each axis.
- For instance, if a line makes an angle of 30 degrees with the x-axis, the direction cosine (l) would be cos(30°), which equals √3/2.
Clarification on Other Options
- Option A talks about tangents, which do not represent direction cosines.
- Option B mentions sines, which represent direction sines, not cosines.
- Option C refers to cotangents, which again do not define direction cosines.
Conclusion
In summary, the direction cosines are indeed the cosines of the angles made with the positive directions of the coordinate axes, confirming that option D is the accurate choice. Understanding this concept is crucial for solving various problems in geometry and physics, especially in the context of JEE.
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Direction cosines of a line area)The tangents of the angles made by the line with the negative directions of the coordinate axes.b)The sines of the angles made by the line with the positive directions of the coordinate axes.c)The cotangents of the angles made by the line with the negative directions of the coordinate axes.d)The cosines of the angles made by the line with the positive directions of the coordinate axes.Correct answer is option 'D'. Can you explain this answer?
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Direction cosines of a line area)The tangents of the angles made by the line with the negative directions of the coordinate axes.b)The sines of the angles made by the line with the positive directions of the coordinate axes.c)The cotangents of the angles made by the line with the negative directions of the coordinate axes.d)The cosines of the angles made by the line with the positive directions of the coordinate axes.Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction cosines of a line area)The tangents of the angles made by the line with the negative directions of the coordinate axes.b)The sines of the angles made by the line with the positive directions of the coordinate axes.c)The cotangents of the angles made by the line with the negative directions of the coordinate axes.d)The cosines of the angles made by the line with the positive directions of the coordinate axes.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction cosines of a line area)The tangents of the angles made by the line with the negative directions of the coordinate axes.b)The sines of the angles made by the line with the positive directions of the coordinate axes.c)The cotangents of the angles made by the line with the negative directions of the coordinate axes.d)The cosines of the angles made by the line with the positive directions of the coordinate axes.Correct answer is option 'D'. Can you explain this answer?.
Direction cosines of a line area)The tangents of the angles made by the line with the negative directions of the coordinate axes.b)The sines of the angles made by the line with the positive directions of the coordinate axes.c)The cotangents of the angles made by the line with the negative directions of the coordinate axes.d)The cosines of the angles made by the line with the positive directions of the coordinate axes.Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction cosines of a line area)The tangents of the angles made by the line with the negative directions of the coordinate axes.b)The sines of the angles made by the line with the positive directions of the coordinate axes.c)The cotangents of the angles made by the line with the negative directions of the coordinate axes.d)The cosines of the angles made by the line with the positive directions of the coordinate axes.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction cosines of a line area)The tangents of the angles made by the line with the negative directions of the coordinate axes.b)The sines of the angles made by the line with the positive directions of the coordinate axes.c)The cotangents of the angles made by the line with the negative directions of the coordinate axes.d)The cosines of the angles made by the line with the positive directions of the coordinate axes.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Direction cosines of a line area)The tangents of the angles made by the line with the negative directions of the coordinate axes.b)The sines of the angles made by the line with the positive directions of the coordinate axes.c)The cotangents of the angles made by the line with the negative directions of the coordinate axes.d)The cosines of the angles made by the line with the positive directions of the coordinate axes.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Direction cosines of a line area)The tangents of the angles made by the line with the negative directions of the coordinate axes.b)The sines of the angles made by the line with the positive directions of the coordinate axes.c)The cotangents of the angles made by the line with the negative directions of the coordinate axes.d)The cosines of the angles made by the line with the positive directions of the coordinate axes.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Direction cosines of a line area)The tangents of the angles made by the line with the negative directions of the coordinate axes.b)The sines of the angles made by the line with the positive directions of the coordinate axes.c)The cotangents of the angles made by the line with the negative directions of the coordinate axes.d)The cosines of the angles made by the line with the positive directions of the coordinate axes.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Direction cosines of a line area)The tangents of the angles made by the line with the negative directions of the coordinate axes.b)The sines of the angles made by the line with the positive directions of the coordinate axes.c)The cotangents of the angles made by the line with the negative directions of the coordinate axes.d)The cosines of the angles made by the line with the positive directions of the coordinate axes.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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