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

ua n dv are two non-collinear unit vectors such that |( hat u+ hat v)/2+ hat uxx hat v|=1. Prove that | hat uxx hat v|=|( hat u- hat v)/2|dot

u and v are two non-collinear unit vectors such that |(widehat u+hat v)/(2)+widehat u xxhat v|=1. Prove that |widehat u xxhat v|=|(widehat u-hat v)/(2)|

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

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors hat(a), hat(b), hat(c) such that hat(a)*hat(b)=hat(b)*hat(c)=hat(c)*hat(a)=(1)/(2). Then, the volume of the parallelopiped is

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors hat(a), hat(b), hat(c) such that hat(a)*hat(b)=hat(b)*hat(c)=hat(c)*hat(a)=(1)/(2). Then, the volume of the parallelopiped is

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors hat(a), hat(b), hat(c) such that hat(a)*hat(b)=hat(b)*hat(c)=hat(c)*hat(a)=(1)/(2). Then, the volume of the parallelopiped is

Let hatu, hatv, hatw be three unit vectors such that hatu+hatv+hatw=hata, hata.hatu=3/2, hata.hatv=7/4 & |hata|=2 , then