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`

the base vectors vec a_(1),vec a_(2),vec longrightarrow3 are given in terms of base vectors vec b_(1),vec b_(2),vec b_(3) as vec a_(1)=2vec b_(1)+3vec b_(2)-vec b_(2)-vec b_(3)+vec a_(2)=vec b_(1)-2vec b_(2)+2vec b_(3) and vec a_(3)=-2vec b_(1)+2vec b_(2)-2vec b_(3) If vec F=3vec b_(1)-vec b_(2)+2vec b_(3), then express vec F in terms of vec a_(1),vec a_(2) and vec a_(3)

The base vectors vec a_ (1), vec a_ (2), vec a_ (3) are given in terms vectors vec b_ (1), vec b_ (2), vec b_ (3) vec a_ (1) = 2vec b_ (1) + 3vec b_ (1) -vec b_ (1), vec a_ (2) = vec a_ (1) -2vec b_ (2) + 2vec b_ (3), vec a_ (3) = - 2vec b_ ( 1) + vec b_ (2) -2vec b_ (3) if vec F_ (1) = 3vec b_ (1) -vec b_ (2) + 2vec b_ (3), Express vec F in terms of vec a_ (1) , vec a_ (2), vec a_ (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

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

If vec a perpvec b, then vector vec v in terms of vec a and vec b satisfying the equations vec v*vec a=0 and vec v*vec b=1 and [vec vvec avec b]=1 is

vec u = vec a-vec b, vec v = vec a + vec b and | vec a | = | vec b | = 2 then | vec u xxvec v | is equal to

For any two vectors vec u and vec v prove that (vec udot v)^(2)+|vec u xxvec v|^(2)=|vec u|^(2)|vec v|^(2)

If vec u,vec v and vec w are three non-copolanar vectors,then prove that (vec u+vec v-vec w)*(vec u-vec v)xx(vec v-vec w)=vec u*vec v*xxvec w

Let vec u and vec v be unit vectors such that vec u xxvec v+vec u=vec w and vec w xxvec u=vec v. Find the value of [vec uvec vvec w]