If `u and v` are two non-collinear unit vectors such that `|vecu × vecv| = ∣ ​ (vecu − vecv) /2 ​ ∣`​ , then the value of ∣ `vecu ×( vecu × vecv) ∣ ^2` is equal to

If vec a and vec b be two non-collinear unit vector such that vec axx( vec axx vec b)=1/2 vec b , then find the angle between vec a and vec b .

If vec a \ a n d \ vec b are two non-collinear unit vector, and ∣ ​ veca + vecb ∣ ​ = 3 ​ then (2 veca −5 vecb ).(3 veca + vecb ) =

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

Let vec u and vec v be unit vectors such that vec uxx vec v+ vec u= vec w and vec wxx vec u= vec v . Find the value of [ vec u \ vec v \ vec w] .

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

Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(veca.vecb)vecb and vecv=vecaxxvecb , then |vecv| is

Let vec aa n d vec b be two non-collinear unit vector. If vec u= vec a-( vec adot vec b) vec ba n d vec v= vec axx vec b ,t h e n| vec v| is a. | vec u| b. | vec u|+| vec udot vec a| c. | vec u|+| vec udot vec b| d. | vec u|+ hat udot| vec a+ vec b|

If veca, vecb and vecc are non -coplanar unit vectors such that vecaxx(vecbxxvecc)=(vecb+vecc)/sqrt2,vecb and vecc are non- parallel , then prove that the angle between veca and vecb is 3pi//4

Let vecu,vecv and vecw be vectors such that vecu+ vecv + vecw =0 if |vecu|= 1, |vecv|=2 and |vecw|=3 then vecu.vecv + vecv .vecw + vecw .vecu is

For many vector vecx , the value of (vecx xxhati)^2+(vecx xxhatj)^2+(vecx xxhatk)^2 is equal to