`(1+|vec u|^2)(1+|vec v|^2)=(1-vec u.vec v)^2+(vec u+vec v+(vec u xx vec v)|^2`

For any two vectors vec ua n d vec v prove that ( vec udot vec v)^2+| vec uxx vec v|^2=| vec u|^2| vec v|^2a n d ( vec1+| vec u|^2)( vec1+| vec v|^2)=(1- vec udot vec v)^2+| vec u+ vec v+( vec uxx vec v)|^2

For any two vectors vec ua n d vec v prove that ( vec udot vec v)^2+| vec uxx vec v|^2=| vec u|^2| vec v|^2a n d ( vec1+| vec u|^2)( vec1+| vec v|^2)=(1- vec udot vec v)^2+| vec u+ vec v+( vec uxx vec v)|^2

For any two vectors vec ua n d vec v prove that ( vec u. vec v)^2+| vec uxx vec v|^2=| vec u|^2| vec v|^2

For any two vectors vec ua n d vec v prove that ( vec u. vec v)^2+| vec uxx vec v|^2=| vec u|^2| vec v|^2

For any two vectors vec ua n d vec v prove that ( vec u . vec v)^2+| vec uxx vec v|^2=| vec u|^2| vec v|^2

For three vectors vec u , vec va n d vec w which of the following expressions is not equal to any of the remaining three ? a. vec u .( vec vxx vec w) b. ( vec vxx vec w). vec u c. vec v.( vec uxx vec w) d. ( vec uxx vec v).vec w

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

For three vectors vec u,vec v and vec w which of the following expressions is not equal to any of the remaining three ? a.vec uvec v xxvec w b.(vec v xxvec w)vec u c.vec vvec u xxvec w d.(vec u xxvec v)vec w

If vec a_|_ vec b , then vector vec v in terms of vec aa n d vec b satisfying the equation s vec v . vec a=0a n d vec v . vec b=1a n d[ vec v vec a vec b]=1 is a. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) b. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) c. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) d. none of these

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