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.
AP PHYSICS – VECTORS 101 BUFFY PEERED INTO
BIOSAFETY CONSIDERATIONS FOR RESEARCH WITH LENTIVIRAL VECTORS DECEMBER 2006
CALCULUS BC WORKSHEET 3 ON VECTORS WORK THE FOLLOWING
Tags: drawn from, vectors, drawn