Question

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 ?

Answer 1

Please see the explanation below.

Explanation:

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)`