The angle that a vector makes when it is parallel to x-axis.

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    Angle Parallel Vector
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Discussion Overview

The discussion revolves around the angles that a displacement vector makes when it is parallel to the x-axis, particularly focusing on vectors positioned above or below the x-axis. Participants explore the implications of these angles in terms of direction and rotation.

Discussion Character

  • Conceptual clarification, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions whether a vector parallel to the x-axis below the x-axis makes an angle of ∏ or -∏, and similarly for a vector above the x-axis.
  • Another participant argues that the angle does not depend on the position relative to the x-axis but rather on the direction of the vector, stating that a vector pointing towards the positive x-axis has an angle of 0, while one pointing towards the negative x-axis has an angle of ∏.
  • Some participants note that ∏ and -∏ represent the same direction on the unit circle but are different in terms of rotation, with ∏ indicating counterclockwise and -∏ indicating clockwise rotation.
  • A later reply acknowledges a previous oversight and thanks others for their responses.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of angles for vectors parallel to the x-axis, particularly regarding the significance of the position of the vector relative to the x-axis and the nature of the angles ∏ and -∏. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are nuances regarding the definitions of angles in relation to direction and rotation that are not fully resolved, particularly in the context of how angles are represented in different quadrants of the unit circle.

Alshia
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If there is a (displacement) vector parallel to the x-axis, and this vector is below the x-axis, is the angle (in radians) made by this vector ∏ or -∏? Why?

If the vector is above the x-axis, what is the angle? Why?
 
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Alshia said:
If there is a (displacement) vector parallel to the x-axis, and this vector is below the x-axis, is the angle (in radians) made by this vector ∏ or -∏? Why?

If the vector is above the x-axis, what is the angle? Why?

The angle does not depend on which side of the x-axis it lies on. It depends on what the direction of the vector is. Say if it were pointing towards positive x axis, then the angle would be 0. If pointing towards negative x-axis then angle would be ∏.

PS : ∏ and -∏ are the same thing :wink:
 
Infinitum said:
PS : ∏ and -∏ are the same thing :wink:
The reference points on the unit circle for the two angles are the same, but the angles are different. An angle of ##\pi## implies counterclockwise rotation; an angle of -##\pi## implies clockwise rotation.
 
Ah, I missed that accidentally. Thanks for the responses.
 
Mark44 said:
The reference points on the unit circle for the two angles are the same, but the angles are different. An angle of ##\pi## implies counterclockwise rotation; an angle of -##\pi## implies clockwise rotation.

Oh, yes. I was only speaking of them in the sense that they would put you in the same direction after rotation. :smile:
 

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