Which of the following relations is true for | vedclass

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Question

$|\hat{ A }+\hat{ B }|=\sqrt{|\hat{ A }|^{2}+|\hat{ B }|^{2}+2|\hat{ A } \| \hat{ B }| \cos 	heta}$

$=\sqrt{1+1+2 \cos 	heta}$

$=\sqrt{2(1+\co

Vedclass · Accepted Answer

$|\hat{ A }-\hat{ B }|=|\hat{ A }+\hat{ B }| 	an \frac{	heta}{2}$

Vedclass · Answer

$|\hat{ A }+\hat{ B }|=\sqrt{|\hat{ A }|^{2}+|\hat{ B }|^{2}+2|\hat{ A } \| \hat{ B }| \cos 	heta}$

$=\sqrt{1+1+2 \cos 	heta}$

$=\sqrt{2(1+\cos 	heta)}$

$=\sqrt{2 	imes 2 \cos ^{2} \frac{	heta}{2}}$

$=2 \cos \frac{	heta}{2}$

$|\hat{ A }-\hat{ B }|=\sqrt{|\hat{ A }|^{2}+|\hat{ B }|^{2}-2|\hat{ A }||\hat{ B }| \cos 	heta}$

$=\sqrt{2-2 \cos 	heta}$

$=2 \sin \frac{	heta}{2}$

$\frac{|\hat{ A }+\hat{ B }|}{|\hat{ A }-\hat{ B }|}=\cot \frac{	heta}{2}$

Which of the following relations is true for two unit vectors $\hat{ A }$ and $\hat{ B }$ making an angle $\theta$ to each other$?$

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