A) \[37{}^\circ \]
B) \[53{}^\circ \]
C) \[{{\cos }^{-1}}\left( -3/4 \right)\]
D) \[{{\cos }^{-1}}\left( -5/12 \right)\]
Correct Answer: C
Solution :
[c] \[\left| \vec{A}+\vec{B} \right|=\frac{\left| \vec{A}-\vec{B} \right|}{2}\] \[{{\left| \vec{A}+\vec{B} \right|}^{2}}=\frac{{{\left| \vec{A}-\vec{B} \right|}^{2}}}{4}\] \[\left( {{A}^{2}}+{{B}^{2}}+2AB\cos \theta \right)=\frac{{{A}^{2}}+{{B}^{2}}-2AB\cos \theta }{4}\] \[\left| {\vec{A}} \right|\,=\,\left| {\vec{B}} \right|\Rightarrow {{A}^{2}}=4{{B}^{2}}\] \[4[4{{B}^{2}}+{{B}^{2}}+2(2B)(B)\cos \theta ]\] \[=4{{B}^{2}}+{{B}^{2}}-2(2B)(B)\cos \theta \] \[4\left( 5{{B}^{2}}+4{{B}^{2}}\cos \theta \right)=5{{B}^{2}}-4{{B}^{2}}\cos \theta \] \[20\cos \theta =-15\] \[\cos \theta =\frac{-3}{4}\]You need to login to perform this action.
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