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When two vectors A and B are drawn from a common point, the angle between them is z

When two vectors A and B are drawn from a common point, the angle between them is ф.

a) Using vector techniques, show that the magnitude of their vector sum is given by

sqrt[A2+B2+2ABcos(ф)]


b) If A and B have the same magnitude, for which value of ф will their vector sum have the same magnitude as A or B?


c) Derive a result analogous to that in part (a) for the magnitude of the vector difference A-B.


d) if A and B have the same magnitude, for what value of ф will A-B have this same magnitude?


For part (a), I drew vectors A and B on a rectangular coordinate where I chose angle α for the angle of A and angle Ө for the angle of B, and angle ф = α- Ө for the angle between A and B. Then the magnitude of A+B=A+B=sqrt[(Ax+Bx)2+(Ay+By)2]=sqrt[A2+B2+2AB(cos α cos Ө+sin α cos Ө)=sqrt[A2+B2+2ABcos(α- Ө)]= sqrt[A2+B2+2ABcos(ф)], where A is the magnitude of A and B is the magnitude of B after the factorization. Is this the proper way to do this?? The answer from my professor isn’t like this.


b) A+A= sqrt[A2+B2+2ABcos(ф)]=>4A2=2A2+2A2cos(ф)=>1=cos(ф)


which means ф= α- Ө =0


does that even make sense??


I think I just interpreted the whole question wrong or something.


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