[" If "a+b+c=alpha d,b+c+d=beta a" and "a,b,c" are non-coplanar vectors,then "],[a+b+c+d=0" ."]

If a +b+c = alphad, b+c+d=beta a and a, b, c are non-coplanar, then the sum of a +b+c+d =

If a +b+c = alphad, b+c+d=beta a and a, b, c are non-coplanar, then the sum of a +b+c+d =

If a +b+c = alphad, b+c+d=beta a and a, b, c are non-coplanar, then the sum of a +b+c+d =

If a +b+c = alphad, b+c+d=beta a and a, b, c are non-coplanar, then the sum of a +b+c+d =

i) bar(a), bar(b), bar(c) are pairwise non zero and non collinear vectors. If bar(a)+bar(b) is collinear with bar(c) and bar(b)+bar(c) is collinear with bar(a) then find the vector bar(a)+bar(b)+bar(c) . ii) If bar(a)+bar(b)+bar(c)=alphabar(d), bar(b)+bar(c)+bar(d)=betabar(a) and bar(a), bar(b), bar(c) are non coplanar vectors, then show that bar(a)+bar(b)+bar(c)+bar(d)=bar(0) .

If vec a, vec b , vec c are three non- coplanar vectors such that vec a + vec b + vec c = alpha vec d and vec b +vec c + vec d = beta vec a, " then " vec a + vec b + vec c + vec d to equal to

If vec a, vec b , vec c are three non- coplanar vectors such that vec a + vec b + vec c = alpha vec d and vec b +vec c + vec d = beta vec a, " then " vec a + vec b + vec c + vec d to equal to

If the four vectors a,b,c,d are coplanar, then (a xx b) xx (c xx d) =