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[" E "],[" 유 "],[" w "],[vec x]

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If vec u, vec v , vec w be vectors such that vecu +vec v + vec w =0 and |vec u | =3, |vec v | = 4, | vec w | = 5 , " then " vec u. vec v + vec v .vec w+ vec w .vec u is equal to : a)47 b)-47 c)0 d)-25

If vec e_1, vec e_2, vec e_3a n d vec E_1, vec E_2, vec E_3 are two sets of vectors such that vec e_idot vec E_j=1,ifi=j and vec e_idot vec E_j=0a n difi!=j , then prove that [ (vec e_1, vec e_2 ,vec e_3)][ (vec E_1, vec E_2, vec E_3) ]=1.

If vec e_1, vec e_2, vec e_3a n d vec E_1, vec E_2, vec E_3 are two sets of vectors such that vec e_idot vec E_j=1,ifi=j and vec e_idot vec E_j=0a n difi!=j , then prove that [ (vec e_1, vec e_2 ,vec e_3)][ (vec E_1, vec E_2, vec E_3) ]=1.

The scalars la n dm such that l vec a+m vec b= vec c ,w h e r e vec a , vec ba n d vec c are given vectors, are equal to

If |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-a)^2|=0 and vectors vec A , vec B ,a n d vec C , w h e r e vec A=a^2 hat i+a hat j+ hat k , etc, are non-coplanar, then prove that vectors vec X , vec Ya n d vec Z ,w h e r e vec X=x^2 hat i+x hat j+ hat k , etc. may be coplanar.

If |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-a)^2|=0 and vectors vec A , vec B ,a n d vec C , w h e r e vec A=a^2 hat i+a hat j+ hat k , etc, are non-coplanar, then prove that vectors vec X , vec Ya n d vec Z ,w h e r e vec X=x^2 hat i+x hat j+ hat k , etc. may be coplanar.

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 .

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)

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)

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