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Vector — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsVector1 Mark
Question
Assertion : If $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$, then angle between $\vec{A}$ and $\vec{B}$ is $90^{\circ}$
Reason $\quad: \quad \vec{A}+\vec{B}=\vec{B}+\vec{A}$
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Answer

(b)$\begin{aligned}& |\vec{A}+\vec{B}|=|\vec{A}-\vec{B}| \\& \Rightarrow A^2+B^2+2 A B \cos \theta=A^2+B^2+2 A B \cos \theta\end{aligned$Hence $\cos \theta=0$ which gives $\theta=90^{\circ}$Also vector addition is commutative.Hence $\vec{A}+\vec{B}=\vec{B}+\vec{A}$.

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