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

Thread starter rannasquaer
Start date Dec 7, 2020
Tags

Orthogonal Projection

AI Thread Summary

The discussion focuses on proving the equation $ v_{1}=V \cos(\psi)+v'_{1} \cos(\theta - \psi) $ related to the orthogonal projections of triangle components. It is established that $ v_{1} $ represents the sum of the orthogonal projections of $ V $ and $ v'_{1} $ onto $ v_{1} $. Participants express difficulty in visualizing and calculating these projections. Clarification on the geometric interpretation and mathematical steps for deriving the projections is sought. Understanding these projections is crucial for validating the given expression.

Dec 7, 2020

rannasquaer

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.

Mathematics news on Phys.org

Dec 7, 2020

Opalg

Gold Member

MHB

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...

View full post »

Thread 'Fixing Things Which Can Go Wrong With Complex Numbers'

Greg tells me the feature to generate a new insight announcement is broken, so I am doing this: https://www.physicsforums.com/insights/fixing-things-which-can-go-wrong-with-complex-numbers/

View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

View full post »