Question

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) $

Answer 1

Answer: (D)

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) $