If ` vec a , vec b ,and vec c` are non-coplanar unit vectors such that ` vec axx( vec bxx vec c)=( vec b+ vec c)/(sqrt(2)), vec b and vec c` are non-parallel, then prove that the angle between ` vec a and vec b, is 3pi//4.`

If vec a , vec b and vec c are non-coplanar unit vectors such that vec axx( vec bxx vec c)=( vec b+ vec c)/(sqrt(2)) , then the angle between vec a and vec b is a. 3pi//4 b. pi//4 c. pi//2 d. pi

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 .

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

Let vec(a).vec(b) and vec(c) be three unit vectors such that vec(a) xx (vec(b) xx vec(c)) = (sqrt3)/(2) (vec(b) + vec(c)) . If vec(b) is not parallel to vec(c) , then the angle between vec(a) and vec(b) is

If vec a , vec b ,a n d vec c are such that [ vec a vec b vec c]=1, vec c=lambda vec axx vec b , , | vec a|=sqrt(2),| vec b|=sqrt(3)a n d| vec c|=1/(sqrt(3)) , then the angle between vec a and vec b is pi/6 b. pi/4 c. pi/3 d. pi/2

If vec a and 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 a , vec b , and 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| .

If vec a , vec b ,a n d vec c are non-zero vectors such that vec a. vec b= vec a. vec c , then find the geometrical relation between the vectors.

If vec a, vec b,vec c and vec d are unit vectors such that (vec a xx vec b) . vec c xx vec d= 1 and vec a.vec c =1/2 then a) vec a, vec b and vec c are non-coplanar b) vec b, vec c ,vec d are non -coplanar c) vec b, vecd are non parallel d) vec a , vec d are parallel and vec b, vec c are parallel

If vec a , vec b , and vec c be non-zero vectors such that no two are collinear or ( vec axx vec b)xx vec c=1/3| vec b|| vec c| vec adot If theta is the acute angle between vectors vec b and vecc , then find the value of sin thetadot