The discussion revolves around the conditions under which the sum of the squares of the magnitudes of the projection vectors of two vectors \( \vec{a} \) and \( \vec{b} \) equals one, specifically when the angle between them is not 90 degrees. Participants are exploring the relationship between these projections and the cosine of the angle between the vectors.
The discussion is ongoing, with participants sharing their interpretations and attempting to clarify the problem. There is recognition of the complexity of the question, and some guidance has been offered regarding the relationship between the projections and the vectors' magnitudes.
Participants are working under the constraint that the angle between the vectors is not 90 degrees, which may influence their reasoning and assumptions about the projections.
anonymoususer said:Homework Statement
The angle between two vectors a and b is ∅, where ∅≠90°. Under what conditions will |Projab|2 + |Projba|2 = 1?
Homework Equations
|Pab|= |\vec{a}\bullet\vec{b}|/|\vec{b}|
|Pba|= |\vec{a}\bullet\vec{b}|/|\vec{a}|
The Attempt at a Solution
I know that |Pab|=|Pba| when |\vec{a}|=|\vec{b}|
I'm not sure where I go from there.
Any help is appreciated, thanks.
Dick said:Looks to me like they just want you to derive an express for cos(∅) in terms of |a| and |b|.
anonymoususer said:I think it's a little more complex than that. I am a little confused on what the question is asking though.