Why Can't Vector Projections Between Two Vectors Be the Same The question is as follows:

Give two reasons why the projection of u onto v is not the same as the projection of v onto u.

I was thinking that the directions of vectors u and v are not the same so that's one way that the projections might differ. Furthermore, the length of the vectors may not be the same as well (given the exception that u and v are unit vectors in which case their length would be 1). 
Are those reasons valid? If not, how can I refine them?  

The projectoin can be the same, if they are equal. When they are not equal, you have two cases:


*

*they are colinear: then the two projections are the identity on both, and so different. 

*they are not colinear: the projection onto $u$ is colinear with $u$, while the projection onto $v$ is colinear with $v$. 
