Vector Sum

The solution can be obtained by using parallelogram law of vector addition .

We know if that if $\overrightarrow { A } ,\overrightarrow { B }$ are two Vectors then the resultant Vector would be

$\left| {\overrightarrow { R } }^{ 2 } \right| = \left|{ \overrightarrow { A } }^{ 2 }\right| + \left|{ \overrightarrow { B } }^{ 2 }\right| +2ABcos\theta$ .

Now We can see that the case would be possible only if

$2\cos\theta = -1$

or $\cos\theta =-1/2$ and $\cos120=-1/2$ . Hence the Angle $\theta\ =120$ .