If `veca,vec b,vec c` are coplanar vectors, then `|(vec a,vec b,vec c),(vec b,vec c,vec a),(vec c,vec a,vec b)|= vec a`

If vec a , vec b , vec c are coplanar vectors, prove that |[vec a, vec b, vec c],[vec a.vec a ,vec a.vec b,vec a.vec c],[vec b.vec a, vec b.vec b, vec b.vec c]|=vec 0 .

If the vectors vec a, vec b, vec c are coplanar, then the value of | (vec a, vec b, vec c), (vec a * vec a, vec a * vec b, vec a * vec c), (vec b * vec a, vec b * vec b, vecb * vec c) | =

If vec a, vec b, vec c are linearly independent vectors and Delta = |(vec a, vec b, vec c), (vec a. vec a, vec a.vec b, veca . vec c), (vec a. vec c, vec b . vecc, vec c. vec c)| then ,

If vec a,vec b, and vec c are three vectors such that vec a xxvec b=vec c,vec b xxvec c=vec a,vec c xxvec a=vec b then prove that |vec a|=|vec b|=|vec c|

If vec a , vec b , vec c are three non-coplanar vectors, prove that [ vec a+ vec b+ vec c vec a+ vec b vec a+ vec c]=-[ vec a vec b vec c]

If vec a, vec b, vec c are non coplanar vectors such that, vec b xx vec c = vec a, vec c xx vec a = vec b, vec a xx vec b = vec c , then |vec a + vec b + vec c| =

veca , vec b , vec c are non-coplanar vectors and x vec a + y vec b + z vec c = vec 0 then

veca , vec b , vec c are non-coplanar vectors and x vec a + y vec b + z vec c = vec 0 then

If vec a, vec b, vec c are three vectors such that vec a . (vec b + vec c) + vec b . (vec c + vec a) + vec c . (vec a + vec b) = 0 and |vec a| = 1, |vec b | = 4, |vec c| = 8 , then |vec a + vec b + vec c| =

(vec a xxvec b)xx(vec b xxvec c)=vec b, where vec a,vec b, and vec c are nonzero vectors,then vec a,vec b, and vec c can be coplanar vec a,vec b, and vec c must be coplanar vec a,vec b, and vec c cannot be coplanar none of these