question_answer

Two vectors of equal magnitude 2 unit lying in the same plane are distributed an angle of\[60{}^\circ \]. The magnitude of their difference would be

A)  \[2\sqrt{3}\,unit\]                         

B)  \[\sqrt{7}\,unit\]

C)  2 unit                   

D)  zero

Correct Answer: B

Solution :

                Consider the vector diagram shown below. Now for the difference OA - OB Now magnitude of \[|OA-OB|\]is \[R=\sqrt{O{{A}^{2}}+O{{B}^{2}}+2(OA)\,(OB)\cos 120{}^\circ }\]     \[=\sqrt{{{2}^{2}}+{{2}^{2}}+2\times -\frac{1}{2}}=\sqrt{7}\,\text{unit}\]