question_answer

Three vectors of equal magnitudes (let P) are lying in a plane such that respective angle between one another is 45°, then the magnitude of these resultants would be

A)  \[\sqrt{3\,(P+1)}\]                         

B)  \[\sqrt{2{{P}^{2}}+3}\]

C)  zero                                     

D)  \[P(\sqrt{2}+1)\]

Correct Answer: D

Solution :

                Let the vectors are OA , OB and OC shown below. Given that, OA = OB = OC = P Clearly, the resultant ofOA and OC willbe in the direction of OB. The magnitude of OA + OC \[=2P\cos 45{}^\circ =P\sqrt{2}\] Now, magnitude of resultant vector along OB is \[P+P\sqrt{2}=P(\sqrt{2}+1)\]