Let ` vec a , vec b , vec c` be three unit vectors and ` vec a . vec b= vec a . vec c=0.` If the angel between ` vec b` and `vec c` is `pi/3` , then find the value of `|[ vec a vec b vec c]|` .

If vec a and vec b be two unit vectors such that vec a+ vec b is also a unit vector, then find the angle between vec a and vec b

The non-zero vectors vec a , vec b and vec c are related by vec a=8 vec b and vec c = −7 vec b , then the angle between vec a and vec c is

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 , vec b ,a n d vec c are there mutually perpendicular unit vectors and vec d is a unit vector which makes equal angles with vec a , vec b ,a n d vec c , the find the value off | vec a+ vec b+ vec c+ vec d|^2dot

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 a, vec b, vec c are three given vectors show that [ vec a + vecb + vec c , vecb + vec c , vec a + vec b + vec c ]=0.

Let vec a , vec b ,a n d 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]^2dot

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 ba n d vec c are unit vectors satisfying | vec a- vec b|^2+| vec b- vec c|^2+| vec c- vec a|^2=9, then |2 vec a+5 vec b+5 vec c| is.

Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b+ vec c= vec x , vec adot vec x=1, vec bdot vec x=3/2,| vec x|=2. Then find the angel between cc and xxdot