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u and v are two non-collinear unit vec...

`u and v` are two non-collinear unit vectors such that `|hat uxx hat v|=|( hat u-hat v)/2|.` Find the value of`| hat uxx(hat uxx hat v)|^2`

Text Solution

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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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