[Grammar] ‘at’ versus ‘by’

[northpath]

Are the prepositions in these sentences interchangeable?
Don’t sit at the window – it’s cold outside.
Please put the vase by the window.
I mean
Don’t sit by the window – it’s cold outside.
Please put the vase at the window.

 

[bhaisahab]

I wouldn't use "at the window" for the vase.