Find $ \ 3 \ $ vectors having same orthogonal projection on $ \vec a=(1,2) \ $.

Question

Find $ \ 3 \ $ vectors having same orthogonal projection on $ \vec a=(1,2) \ $.

Answer:

Suppose I take a vector $ \vec b=(2,1) \ $ . Then the orthogonal projection is

$ (|\vec b| \cos \theta ) \frac{\vec a}{|\vec a |} \ $

But how to find more two vectors having same orthogonal projection on $ \vec a \ $ as $ \vec b \ $ .

Is one of them $ -\vec b \ $ ?

Please help me .

Answer 1

Yes one of them is $-b$, for finding other vectors, just assume $c=(a,x) \ a\ is \ a \ constant$. Use the formula that you have written to find $x$ so that $c$ also have the same projection.