Condition for Equal Magnitudes of Projection Vectors?

[anonymoususer]

Homework Statement

The angle between two vectors a and b is ∅, where ∅≠90°. Under what conditions will |Proj_ab|² + |Proj_ba|² = 1?

Homework Equations

|P_ab|= |\vec{a}\bullet\vec{b}|/|\vec{b}|

|P_ba|= |\vec{a}\bullet\vec{b}|/|\vec{a}|

The Attempt at a Solution

I know that |P_ab|=|P_ba| when |\vec{a}|=|\vec{b}|

I'm not sure where I go from there.

Any help is appreciated, thanks.

 

[Dick]

Homework Statement

The angle between two vectors a and b is ∅, where ∅≠90°. Under what conditions will |Proj_ab|² + |Proj_ba|² = 1?

Homework Equations

|P_ab|= |\vec{a}\bullet\vec{b}|/|\vec{b}|

|P_ba|= |\vec{a}\bullet\vec{b}|/|\vec{a}|

The Attempt at a Solution

I know that |P_ab|=|P_ba| when |\vec{a}|=|\vec{b}|

I'm not sure where I go from there.

Any help is appreciated, thanks.

Looks to me like they just want you to derive an express for cos(∅) in terms of |a| and |b|.

 

[anonymoususer]

Looks to me like they just want you to derive an express for cos(∅) in terms of |a| and |b|.

I think it's a little more complex than that. I am a little confused on what the question is asking though.

 

[Dick]

I think it's a little more complex than that. I am a little confused on what the question is asking though.

I worked through it and that's the only thing I can figure they could be asking.