MHB Proving Orthogonal Projection of Triangle V, v'_{1}

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SUMMARY

The discussion focuses on proving the orthogonal projection of triangle V, specifically the equation \( v_{1}=V \cos(\psi)+v'_{1} \cos(\theta - \psi) \). It establishes that \( v_{1} \) represents the sum of the orthogonal projections of both \( V \) and \( v'_{1} \) onto \( v_{1} \). Participants emphasize the need for clarity in the projection calculations to validate this expression. The conversation highlights the importance of understanding trigonometric functions in the context of vector projections.

PREREQUISITES
  • Understanding of vector projections in geometry
  • Familiarity with trigonometric functions, specifically cosine
  • Knowledge of triangle properties and relationships
  • Basic skills in mathematical proof techniques
NEXT STEPS
  • Study vector projection techniques in Euclidean geometry
  • Learn about trigonometric identities and their applications in vector analysis
  • Explore mathematical proof strategies for geometric theorems
  • Investigate the properties of triangles in relation to vector components
USEFUL FOR

Mathematicians, geometry students, and anyone interested in vector analysis and geometric proofs will benefit from this discussion.

rannasquaer
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Given the triangle above where $$V < v'_{1}$$, prove that the \[ v_{1}=V \cos(\psi)+v'_{1} \cos(\theta - \psi) \]

It is said that $$v_{1}$$ is equal to the sum of the orthogonal projections on $$v_{1}$$ of $$V$$ and of $$v'_{1}$$ and that is precisely the expression that show. But I couldn't see how to make the projection and the calculations.
 
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