Vectors vec{A} and vec{B} are such that |vec{A}+vec{B}|=|vec{A}-vec{B}| angle between two vectors is

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3-1.Vectors

hard

The vectors $\vec{A}$ and $\vec{B}$ are such that

$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$

The angle between the two vectors is

$60$

$75$

$45$

$90$

(AIIMS-2019) (AIPMT-1996) (AIPMT-2006) (AIPMT-1991) (AIIMS-2016)

The formula for $|\vec{A}+\vec{B}|^{2}$ is,

$|\vec{A}+\vec{B}|^{2}=|\vec{A}|^{2}+|\vec{B}|^{2}+2 \vec{A} \cdot \vec{B}$

$=A+B+2 A B \cos \theta$ And The formula for $|\vec{A}-\vec{B}|^{2}$ is,

$|\vec{A}-\vec{B}|^{2}=|\vec{A}|^{2}+|\vec{B}|^{2}-2 \vec{A} \cdot \vec{B}$

$=A+B-2 A B \cos \theta$

It is given that,

$|\vec{A}+\vec{B}|^{2}=|\vec{A}-\vec{B}|^{2}$

$A+B+2 A B \cos \theta=A+B-2 A B \cos \theta$

$4 A B \cos \theta=0$

$\cos \theta=0$

$\theta=90^{\circ}$

Standard 11

Physics

easy

medium

medium

medium

hard