Find 3-dimensional vectors `vec v_1,vec v_2,vec v_3` satisfying `vec v_1* vec v_1=4,vec v_1* vec v_2=-2,vec v_1* vec v_3=6, vec v_2* vec v_2=2 , vec v_2 *vec v_3=-5,vec v_3* vec v_3=29`

If vec v_1= (2,-3) , vec v_2=(0,1) and vec v_3=(-1,6) , find a unit vector parallel to vec v_1+2 vec v_2-vec v_3 .

If vec a, vec b, vec c are non-coplanar vectors and vec v * vec a = vec v * vec b = vec v * vec c = 0, then vec v must be a

Let vec u,vec v and vec w be vector such vec u+vec v+vec w=vec 0* If |vec u|=3,|vec v|=4 and |vec w|=5, then find vec u.vec v+vec v*vec w+vec w*vec u

Let vec u , vec v and vec w be vector such vec u+ vec v+ vec w= vec0 . If | vec u|=3,| vec v|=4 and | vec w|=5, then find vec u . vec v+ vec v . vec w+ vec w . vec u .

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

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

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