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

Explanation

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|`