The resultant of and makes an angle α with and β with

Let us consider and along two sides of the parallelogram and the resultant vector along the diagonal of parallelogram. Now if we take the component of along we have B and component of perpendicular to we get A as illustrated above.

Now consider OAX, ∴ AX =OA=|A|

Now consider AXR, ,∴ XR=OB=|B|

In AXR, if we apply the Pythagoras theorem, we get

,∴ , |A|=|B|

Thus, we have , now if ,,{

,∴ , implies |A|>|B| for .

Hence option C satisfies our condition best.