- #1
Gurasees
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Can we find the angle between resultant and one of its vectors without breaking into components?
Angle between resultant and vector
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SUMMARY
The discussion centers on determining the angle between a resultant vector and one of its component vectors without decomposing them into components. It is established that the angle can be calculated using the cosine law, specifically the formula \(\cos(\phi) = \frac{\vec{A} \cdot \vec{B}}{|\vec{A}||\vec{B}|}\). While using components is often the preferred method for convenience, alternative approaches such as basic trigonometry can also be employed. The conversation emphasizes that this topic is fundamentally mathematical rather than physical.
PREREQUISITES- Understanding of vector notation and operations
- Familiarity with the cosine law in trigonometry
- Knowledge of inner product calculations
- Basic principles of coordinate systems
- Study the cosine law in detail, particularly in vector contexts
- Learn about calculating inner products of vectors
- Explore alternative coordinate systems beyond Cartesian
- Investigate practical applications of vector angles in physics
Mathematicians, physics students, and anyone interested in vector analysis and trigonometry will benefit from this discussion.
- #2
sophiecentaur
Science Advisor
Homework Helper
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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. 
- #3
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Gurasees said:
Sure, if you think using sine and cosine laws are easier. It usually isn’t.
This is also a math question, not physics.
Zz.
- #4
A.T.
Science Advisor
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How are the vectors given, if not as components? How many vectors are added to get the resultant vector?Gurasees said:
- #5
Svein
Science Advisor
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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.Gurasees said:
- #6
Gurasees
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- 1
Thank yousophiecentaur 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.
- #7
Gurasees
- 50
- 1
Thank youSvein said:
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