If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, t

Question

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is\

Professor PC Thomas Classes · Answer

(d) : Let the two vectors be $\vec{A}$ and $\vec{B}$. Then, magnitude of sum of $\vec{A}$ and $\vec{B}$,\ $|\vec{A}+\vec{B}|=\sqrt{A^{2}+B^{2}+2 A B \cos 	heta}$\ and magnitude of difference of $\vec{A}$ and $\vec{B}$\ $|\vec{A}-\vec{B}|=\sqrt{A^{2}+B^{2}-2 A B \cos 	heta},|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$ (given)\ or $\sqrt{A^{2}+B^{2}+2 A B \cos 	heta}=\sqrt{A^{2}+B^{2}-2 A B \cos 	heta}$\ $\Rightarrow 4 A B \cos 	heta=0 \quad \because 4 A B 
eq 0, 	herefore \cos 	heta=0$ or $	heta=90^{\circ}$\