When two vectors A and B are drawn from a common point, the angle between them is ф. Using vector techniques, how to show that the magnitude of their vector sum is given by √A^2 + B^2 - 2AB cos ?

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Answer 1 · 2018-06-25T15:13:39

Please see the explanation below.

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The resultant of the vector addition is calculated with the cosine rule

$R^2=A^2+B^2-2ABcos(180-phi)$

$cos(180-phi)=cos180cosphi+sin180sinphi$

$=-1*cosphi+0*sinphi$

$=-cosphi$

Therefore,

$R^2=A^2+B^2-2AB(-cosphi)$

$=A^2+B^2+2ABcosphi$

So,

$R=sqrt(A^2+B^2+2ABcosphi)$