If `vec a`,`vec b`,`vec c ` are three non-coplanar vectors and `vec d* vec a = vec d* vec b= vec d* vec c= 0` then show that `vec d` is zero vector.

If vec a , vec b ,a n d vec c are three non-coplanar vectors, then find the value of ( vec adot( vec bxx vec c))/( vec b dot( vec cxx vec a))+( vec b dot( vec cxx vec a))/( vec c dot( vec axx vec b))+( vec c dot( vec bxx vec a))/( vec a dot( vec bxx vec c))dot

Let vec a , vec b , vec c are three non-zero vectors such that vec axx vec b= vec ca n d vec bxx vec c= vec a ; prove that vec a , vec b , vec c are mutually at righ angles such that | vec b|=1a n d| vec c|=| vec a|dot

If vec a , vec b , vec c are vectors such that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec c , vec a!= vec0, then show that vec b= vec c

If vec a,vec b,vec c are three vectors such that vec a=vec b+vec c and the angle between vec b and vec c is pi/2, then

If vec a , vec b and vec c are three proper vectors such that vec a * vec b=vec c , vec b*vec c=vec a . Prove that vec a , vec b , vec c are mutually at right angles and |quad vec b|=1 ,|quad vec c|=|quad vec a|.

Let vec a , vec b , vec c , be three non-zero vectors. If vec a .(vec bxx vec c)=0 and vec b and vec c are not parallel, then prove that vec a=lambda vec b+mu vec c ,w h e r elambda are some scalars dot

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 u , vec v and vec w are three non-coplanar vectors, then prove that ( vec u+ vec v- vec w)dot [( vec u- vec v)xx( vec v- vec w)] = vec u dot (vec v xx vec w)

Prove that if vec a,vec b,vec c and vec d are any four vectors, then (vec a xx vec b)*(vec c xx vec d)= [[vec a* vec c vec b* vec c], [vec a* vec d vec b* vec d]]

If a, b and c are non-coplanar vectors and d=lambda vec a+mu vec b+nu vec c , then lambda is equal to