If `vec a,vc b and vec c` are non-coplanar vectors, then show that `vec a+vec b`,`vec b+vec c` and `vec c +vec a` are also non-coplanar

If vec a, vec b, vec c non zero coplanar vectors, then, [2 vec a - vec b 3 vec b - vec c 4 vec c - vec a] =

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 and vec c are non coplanar unit vectors such that vec a xx (vec b xx vec c) = (vec b + vec c)/sqrt2 , then

For any three vectors vec a,vec b and vec c , show that vec a- vec b,vec b- vec c and vec c- vec a are coplanar.

If the three vectors vec a,vec b,vec c are coplanar, prove that the vectors vec a+vec b,vec b+vec c and vec c+vec a are also coplanar.

If vec a , vec b and vec c are non-coplanar vectors, prove that vectors 3vec a-7 vec b-4 vec c ,3 vec a -2 vec b+ vec c and vec a + vec b +2 vec c are coplanar.

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 ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a