Question

. Show that the magnitude of the resultant vector C is given by the law of cosines
C = A2 + B2 - 2AB cose​

Answer 1

C=(A-B)2 cose.........

Answer 2

Show that the magnitude of the resultant vector C is given by the law of cosines  $C^2=\sqrt{A^2+B^2-2AB}$

Proof :-

let if possible that-

A and B be two straight vectors having different magnitude and making an angle of 180 degree to each other.

therefore,  

θ = π

so, from the law of vector addition, resultant of these two vector is given by;

$R=\sqrt{A^2+B^2+2ABcos\theta}$

since, it is given that C is the resultant vector and $\theta = \pi$

therefore,

$C=\sqrt{A^2+B^2+2ABcos(\pi)} \\\\C=\sqrt{A^2+B^2+2AB(-1)}\\\\C=\sqrt{A^2+B^2-AB}$

Hence, proved.