These seem to be interchangeable. Are these both grammatically correct? Is there any difference at all?
When are "at" and "towards" interchangeable?
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There is a slight difference in meaning between 'at' and 'towards'. 'At' gives an aggressive sense, eg 'His snide remarks were directed at her.' 'Towards' is more neutral, eg 'We must direct our focus towards a more practical aspect of the issue'. I am not sure whether they are interchangeable, I wouldn't use them as such.