Stupid Question About Finding the Angle of a Vector

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SUMMARY

The discussion centers on calculating the angle of rotation of a vector in the first quadrant of the x-y plane. The user seeks to determine the angle between the original vector and its new position after rotation, given the initial and terminal points of both vectors. The solution involves using the dot product to find the angle of rotation, which is a fundamental concept in vector mathematics.

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  • Understanding of vector representation in the Cartesian coordinate system
  • Knowledge of the dot product and its geometric interpretation
  • Familiarity with trigonometric functions, particularly cosine
  • Basic skills in manipulating angles and radians
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  • Study the properties and applications of the dot product in vector mathematics
  • Learn how to calculate angles between vectors using the formula: θ = cos⁻¹((A·B) / (|A||B|))
  • Explore vector rotation techniques in 2D space
  • Investigate the use of trigonometric identities in solving vector-related problems
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Saladsamurai
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:smile: Okay then!

Let's say we are ONLY working in the 1st Quadrant of the x-y plane. I have some vector in that region that makes some angle with the +x axis. I then rotate that vector through some angle.

The initial points of the vector before and after are coincident, i.e. I only move the terminal end to some new point while maintaining the vectors magnitude.

I know the initial point, I know the terminal points of both the original and new vector.

I now need the angle that I must have rotated through to get to the new point.

Is this a dot product problem?
 
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:smile: Alrighty-then!
 

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