Need help with Vector Question: 13 a) ii) from NEAP paper (1 Viewer)

[Etan1827]

Hey all, just wondering if you could please help me on this question. Kinda clueless on what to do. The question is 13 a) ii).

 

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(I just typed this up real quick so idk if i made a mistake or not I will relook through it now, hopefully this makes sense)

So, when the magnitude of (p + q) is a minimum is when q is antiparallel to p (which just means that p is parallel to q but they point in opposing directions), as you would have seen in (i). So, since the magnitude of q is 20, then q = -20(p̂) = -(20/17)p. So, a = p + q = p -(20/17)p = -(3/17)p which can easily be calculated since that they gave u what p is.

(just to clarify: 17 is the magnitude of p)