Given three vectors `vec V1=ahati+bhatj+chatk; vec V2=bhati+chatj+ahatk; vec V3=chati+ahatj+bhatk` In which of the following conditions `vec V1,vec V2 and vec V3` are linearly independent?

Given three vectors vec V1=ahat i+bhat j+chat k;vec V2=bhat i+chat j+ahat k;vec V3=chat i+ahat j+bhat k In which of the following conditions vec V1,vec V2 and vec V3 are linearly independent?

Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(gamma)=chati+ahatj+bhatk be three coplnar vectors with a!=b , and vecv=hati+hatj+hatk . Then vecv is perpendicular to

Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(gamma)=chati+ahatj+bhatk be three coplnar vectors with a!=b , and vecv=hati+hatj+hatk . Then vecv is perpendicular to

Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(gamma)=chati+ahatj+bhatk be three coplnar vectors with a!=b , and vecv=hati+hatj+hatk . Then vecv is perpendicular to

Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(gamma)=chati+ahatj+bhatk be three coplnar vectors with a!=b , and vecv=hati+hatj+hatk . Then vecv is perpendicular to

Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(gamma)=chati+ahatj+bhatk be three coplnar vectors with a!=b , and vecv=hati+hatj+hatk . Then vecv is perpendicular to

Taking vec v_1= hat i+ 2 hat j- hat k , vec v_2= 2 hat i- hat j+ hat k and vec v_3= hat i+ hat j+ hat k verify that (vec v _1*vec v_2 ) vec v_3 != vec v_1(vec v _2* vec v_3) .

Let vec(alpha)=ahati+bhatj+chatk,vecb=bhati+chatj+ahatk and vec(gamma)=chati+ahatj+bhatk are three coplanar vectors with a!=b and vec(gamma)=hati+hatj+hatk . Then vec(gamma) is perpendicular to

Let vec(V_(1))=hati+ahatj+hatk, vec(V_(2))=hatj+ahatk and vec(V_(3))=ahati+hatk, AA a gt 0. If [(vec(V_(1)),vec(V_(2)),vec(V_(3)))] is minimum, then the value of a is

Let vec(V_(1))=hati+ahatj+hatk, vec(V_(2))=hatj+ahatk and vec(V_(3))=ahati+hatk, AA a gt 0. If [(vec(V_(1)),vec(V_(2)),vec(V_(3)))] is minimum, then the value of a is