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western50 · Jan 27, 2011, 12:53 AM

Assume that a and b are nonzero vectors in 3 dimensional. Is it ever the cause that projection a on b =projection b on a? If so, exactly when does this occur? The condition should be both necessary and sufficient.

I think that there would be case like that, and I am thinking that can two vectors that made 90 degree work, such as I=(1,0), and j=(0,1), and the projection a on b =projection b on a would = 0? But what would a "0" in projection mean?
Or is there a better example on when does that occur?

anadoingtaxes · Feb 13, 2011, 07:34 PM

Try also with the vector b being a multiple of the vector a, for example, b=2a. What happens then?

ebaines · Feb 14, 2011, 11:12 AM

Consider the formula for the magnitude of the projection of $\vec a$ on $\vec b$ : it's $|a| \cos \theta$ . Conversely, the projection of $\vec b$ on $\vec a$ is $|b| \cos \theta$ . So for the two projections to be equal in magnitude you must have:

$<br /> |a| \cos \theta = {|b| \cos \theta <br />$

Can you think of coditions for either |a| and |b|or angle $\theta$ that make this true?