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In a plane, line X is perpendicular to line Y and parallel to line Z; line U is perpendicular to both lines V and W; line X is perpendicular to line V. Which one of the following statements is correct?
- a)Z, U and W are parallel.
- b)X, V and Y are parallel.
- c)Z, V and U are all perpendicular to W.
- d)Y, V and W are parallel.
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a plane, line X is perpendicular to line Y and parallel to line Z; ...
The correct option is D.
From the above diagram, it is clear that Y, V and W are parallel.
From the above diagram, it is clear that Y, V and W are parallel.
Most Upvoted Answer
In a plane, line X is perpendicular to line Y and parallel to line Z; ...
Explanation:
Given:
- Line X is perpendicular to line Y and parallel to line Z.
- Line U is perpendicular to both lines V and W.
- Line X is perpendicular to line V.
Analysis:
Let's analyze the given information step by step.
1. Line X is perpendicular to line Y and parallel to line Z:
- Line X is perpendicular to line Y, which means that the angle between line X and line Y is 90 degrees.
- Line X is parallel to line Z, which means that the angle between line X and line Z is also 90 degrees.
2. Line U is perpendicular to both lines V and W:
- This implies that the angle between line U and line V is 90 degrees.
- Similarly, the angle between line U and line W is also 90 degrees.
3. Line X is perpendicular to line V:
- This means that the angle between line X and line V is 90 degrees.
Conclusion:
Based on the given information and the analysis, we can conclude the following:
a) Z, U, and W are parallel:
- We do not have any information that directly supports this statement. Therefore, option A is incorrect.
b) X, V, and Y are parallel:
- Line X is perpendicular to line Y, so they cannot be parallel. Therefore, option B is incorrect.
c) Z, V, and U are all perpendicular to W:
- We know that line U is perpendicular to line W, but we do not have any direct information about the relationship between line Z and line W. Therefore, option C is incorrect.
d) Y, V, and W are parallel:
- We know that line X is perpendicular to line Y and line X is also perpendicular to line V. Therefore, line Y and line V are parallel.
- Line U is perpendicular to line W, which means that line W is perpendicular to line U.
- Since line Y is parallel to line V and line W is perpendicular to line U, we can conclude that line Y, line V, and line W are parallel.
- Therefore, option D is correct.
Final Answer:
Option D is the correct answer.
Given:
- Line X is perpendicular to line Y and parallel to line Z.
- Line U is perpendicular to both lines V and W.
- Line X is perpendicular to line V.
Analysis:
Let's analyze the given information step by step.
1. Line X is perpendicular to line Y and parallel to line Z:
- Line X is perpendicular to line Y, which means that the angle between line X and line Y is 90 degrees.
- Line X is parallel to line Z, which means that the angle between line X and line Z is also 90 degrees.
2. Line U is perpendicular to both lines V and W:
- This implies that the angle between line U and line V is 90 degrees.
- Similarly, the angle between line U and line W is also 90 degrees.
3. Line X is perpendicular to line V:
- This means that the angle between line X and line V is 90 degrees.
Conclusion:
Based on the given information and the analysis, we can conclude the following:
a) Z, U, and W are parallel:
- We do not have any information that directly supports this statement. Therefore, option A is incorrect.
b) X, V, and Y are parallel:
- Line X is perpendicular to line Y, so they cannot be parallel. Therefore, option B is incorrect.
c) Z, V, and U are all perpendicular to W:
- We know that line U is perpendicular to line W, but we do not have any direct information about the relationship between line Z and line W. Therefore, option C is incorrect.
d) Y, V, and W are parallel:
- We know that line X is perpendicular to line Y and line X is also perpendicular to line V. Therefore, line Y and line V are parallel.
- Line U is perpendicular to line W, which means that line W is perpendicular to line U.
- Since line Y is parallel to line V and line W is perpendicular to line U, we can conclude that line Y, line V, and line W are parallel.
- Therefore, option D is correct.
Final Answer:
Option D is the correct answer.
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In a plane, line X is perpendicular to line Y and parallel to line Z; line U is perpendicular to both lines V and W; line X is perpendicular to line V. Which one of the following statements is correct?a)Z, U and W are parallel. b)X, V and Y are parallel. c)Z, V and U are all perpendicular to W. d)Y, V and W are parallel.Correct answer is option 'D'. Can you explain this answer?
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In a plane, line X is perpendicular to line Y and parallel to line Z; line U is perpendicular to both lines V and W; line X is perpendicular to line V. Which one of the following statements is correct?a)Z, U and W are parallel. b)X, V and Y are parallel. c)Z, V and U are all perpendicular to W. d)Y, V and W are parallel.Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a plane, line X is perpendicular to line Y and parallel to line Z; line U is perpendicular to both lines V and W; line X is perpendicular to line V. Which one of the following statements is correct?a)Z, U and W are parallel. b)X, V and Y are parallel. c)Z, V and U are all perpendicular to W. d)Y, V and W are parallel.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a plane, line X is perpendicular to line Y and parallel to line Z; line U is perpendicular to both lines V and W; line X is perpendicular to line V. Which one of the following statements is correct?a)Z, U and W are parallel. b)X, V and Y are parallel. c)Z, V and U are all perpendicular to W. d)Y, V and W are parallel.Correct answer is option 'D'. Can you explain this answer?.
In a plane, line X is perpendicular to line Y and parallel to line Z; line U is perpendicular to both lines V and W; line X is perpendicular to line V. Which one of the following statements is correct?a)Z, U and W are parallel. b)X, V and Y are parallel. c)Z, V and U are all perpendicular to W. d)Y, V and W are parallel.Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a plane, line X is perpendicular to line Y and parallel to line Z; line U is perpendicular to both lines V and W; line X is perpendicular to line V. Which one of the following statements is correct?a)Z, U and W are parallel. b)X, V and Y are parallel. c)Z, V and U are all perpendicular to W. d)Y, V and W are parallel.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a plane, line X is perpendicular to line Y and parallel to line Z; line U is perpendicular to both lines V and W; line X is perpendicular to line V. Which one of the following statements is correct?a)Z, U and W are parallel. b)X, V and Y are parallel. c)Z, V and U are all perpendicular to W. d)Y, V and W are parallel.Correct answer is option 'D'. Can you explain this answer?.
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