`hatu and hat v` are two non-collinear unit vectors such that `|(hatu+hatv)/2+hatuxxvecv|=1`. Prove that `|hatuxxhatv|=|(hatu-hatv)/2|`

`hatu and hat v` are two non-collinear unit vectors such that `|(hatu+

1.	`hatu and hat v` are two non-collinear unit vectors such that `\|(hatu+hatv)/2+hatuxxvecv\|=1`. Prove that `\|hatuxxhatv\|=\|(hatu-hatv)/2\|`
Answer» Given that `\|(hatu+hatv)/2+hatuxxhatv\|=1` ` \|(hatu+hatv)/2+hatuxxhatv\|^(2)=1` `(2+2costheta)/4+sin^(2)theta=1` `cos^(2)(theta /2)=cos^(2)theta` `theta=npi+-theta/2,n inZ` `(2pi)/3` `\|hatuxxhatv\|=sin((2pi)/3)=sin (pi/3)=\|(hatu-hatv)/2\|`

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`hatu and hat v` are two non-collinear unit vectors such that `|(hatu+hatv)/2+hatuxxvecv|=1`. Prove that `|hatuxxhatv|=|(hatu-hatv)/2|`

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