Angle between resultant and vector

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    Angle Resultant Vector
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Discussion Overview

The discussion revolves around the question of whether the angle between a resultant vector and one of its component vectors can be determined without breaking the vectors into their components. The scope includes mathematical reasoning and applications of trigonometry in vector analysis.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that using trigonometric laws, such as the sine and cosine laws, can allow for finding the angle without breaking into components, although they note this may not be the easiest method.
  • Others argue that a coordinate system is necessary, but it does not have to be Cartesian, and that basic trigonometry can suffice for calculating angles and sides of triangles formed by vectors.
  • One participant states that the angle between two vectors can be mathematically expressed using the cosine of the angle, defined by the dot product of the vectors and their magnitudes, but leaves the calculation as an exercise for the student.
  • There is a repeated emphasis on the convenience of using components for such calculations, despite the possibility of alternative methods.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of using components versus alternative methods for finding the angle, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

Some assumptions regarding the representation of vectors and the specific conditions under which the angle is calculated are not fully clarified, leaving the discussion open to interpretation.

Gurasees
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Can we find the angle between resultant and one of its vectors without breaking into components?
 
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You have to use some co ordinate system but Cartesian is not necessary. Working out the sides and angles of a triangle, given a side, side and included angle is basic trig. so you don't have to use components. But 20 million flies can't be wrong and using components is usually the most convenient way. :smile:
 
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Gurasees said:
Can we find the angle between resultant and one of its vectors without breaking into components?

Sure, if you think using sine and cosine laws are easier. It usually isn’t.

This is also a math question, not physics.

Zz.
 
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Gurasees said:
Can we find the angle between resultant and one of its vectors without breaking into components?
How are the vectors given, if not as components? How many vectors are added to get the resultant vector?
 
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Gurasees said:
Can we find the angle between resultant and one of its vectors without breaking into components?
Mathematically yes, since the angle between the vectors A and B is given by \cos(\phi)=\frac{\vec{A}\cdot \vec{B}}{\vert \vec{A}\vert\vert \vec{B}\vert}. Calculating the inner product of two vectors is left as an assignment for the student.
 
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sophiecentaur said:
You have to use some co ordinate system but Cartesian is not necessary. Working out the sides and angles of a triangle, given a side, side and included angle is basic trig. so you don't have to use components. But 20 million flies can't be wrong and using components is usually the most convenient way. :smile:
Thank you
 
Svein said:
Mathematically yes, since the angle between the vectors A and B is given by \cos(\phi)=\frac{\vec{A}\cdot \vec{B}}{\vert \vec{A}\vert\vert \vec{B}\vert}. Calculating the inner product of two vectors is left as an assignment for the student.
Thank you
 

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