Explanation

(b) Let $\widehat{A} + \widehat{B} = \widehat{R}$ then using parallelogram law of vectors we have
$1 = \left( 1^{2} + 1^{2} + 2.1.1\ cos\theta \right)^{1/2}$
or $1 = 2(1 + \ cos\theta)$
or $\frac{1}{2} - 1 = \ cos\theta$
or $cos\theta = - \frac{1}{2} = cos120{^\circ}$
or $\theta = 120{^\circ}$
$\therefore\ \left| \widehat{A} - \widehat{B} \right| = \left| \widehat{A} + ( - \widehat{B}) \right|$.
Now the angle between $\widehat{A}\ \ \ and\ \ - \widehat{B}$ is 60${^\circ}$
The resultant of $\left| \widehat{A} + ( - \widehat{B}) \right|$
$\left( 1^{2} + 1^{2} + 2 \times 1 \times 1 \times \cos 60{^\circ} \right)^{1/2}$
=$\sqrt{3}$