If ` vec aa n d vec b` are unequal unit vectors such that `( vec a- vec b)xx[( vec b+ vec a)xx(2 vec a+ vec b)]= vec a+ vec b ,` then angle `theta` between ` vec aa n d vec b` is `0` b. `pi//2` c. `pi//4` d. `pi`

If vec aa n d vec b are unit vectors such that ( vec a+ vec b).(2 vec a+3 vec b)xx(3 vec a-2 vec b)=0 , then angle between veca and vec b is a. 0 b. pi//2 c. pi d. indeterminate

If vec aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .

If | vec a|+| vec b|=| vec c|a n d vec a+ vec b= vec c , then find the angle between vec aa n d vec bdot

If vec a , vec b ,a n d vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c|dot

If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c =0 , find the value of vec a.vec b+ vec b .vec c + vec c. vec a .

If vec aa n d vec b are two vectors, such that vec adot vec b<0a n d| vec adot vec b|=| vec axx vec b|, then the angle between vectors vec aa n d vec b is pi b. 7pi//4 c. pi//4 d. 3pi//4

Let vec aa n d vec b be unit vectors such that | vec a+ vec b|=sqrt(3) . Then find the value of (2 vec a+5 vec b)dot(3 vec a+ vec b+ vec axx vec b)dot

If vec a , vec b ,a n d vec c are non-coplanar unit vectors such that vec axx( vec bxx vec c)=( vec b+ vec c)/(sqrt(2)), vec ba n d vec c are non-parallel, then prove that the angel between vec aa n d vec bi s3pi//4.

If three unit vectors vec a , vec b ,a n d vec c satisfy vec a+ vec b+ vec c=0, then find the angle between vec aa n d vec bdot

If vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot