If `vec r* vec a =0 = vec r* vec b` ,where `vec a and vec b` are non-coplanar vectors then

Solve the vector equation vec r xx vec a + k vec r = vec b , where vec a, vec b are two non-collinear vectors and k is any scalar.

Prove the following : vec a * (vec a xx vec b) = 0 , where are vec a and vec b are any two vectors.

If vec r* vec a =0 = vec r* vec b =0 and also vec r* vec c =0 for some non-zero vector vec r , then the value of vec a*(vec b xx vec c) is........

What is the value of [vec a vec b vec c] if vec a, vec b, vec c are non-zero coplanar vectors ?

If vec a* vec a =0 and vec a* vec b =0 , then what can be concluded about the vector vec b ?

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

If (vec a+ vec b)*(vec a- vec b)=0 and |vec a|=5 , find |vec b| .

If vec c=3vec a+ 4vec b and 2vec c=vec a-vec 3b then show that vec c and vec a are like vectors and |quad vec c|>|quad vec a| .

Incase of each of the following statements, state whether it is true or false : If |vec a+ vec b| =|vec a- vec b| then the vectors vec a and vec b are orthogonal.

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 angel between vec a and vec b, is 3pi//4.