Show that `vec(a), vec(b), vec(c )` are coplanar if and only if `vec(a) + vec(b), vec(b) + vec(c ), vec( c) + vec(a)` are coplanar

Show that the vectors vec a - vec b, vec b - vec c , vec c - vec a are coplaner.

Show that vectors vec a ,\ vec b ,\ vec c are coplanar if vec a+ vec b ,\ vec b+ vec c ,\ vec c+ vec a are coplanar.

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 non coplanar non-zero vectors such that vec( b) xxvec( c) = vec( a ), vec( a ) xx vec( b) =vec( c ) and vec( c ) xx vec( a ) = vec ( b ) , then which of the following is not true

Show that the vectors vec a , vec b and vec c are coplanar if vec a+ vec b , vec b+ vec c and vec c+ vec a are coplanar.

If vec(a) , vec( b) and vec( c ) are unit vectors such that vec(a) + vec(b) + vec( c) = 0 , then the values of vec(a). vec(b)+ vec(b) . vec( c )+ vec( c) .vec(a) is

Prove that vec(a). {(vec(b) + vec(c)) xx (vec(a) + 2vec(b) + 3vec(c))} = [vec(a) vec(b) vec(c)] .

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

If vec(a)+vec(b)+vec(c )=0 " and" |vec(a)|=3,|vec(b)|=5, |vec(c )|=7 , then find the value of vec(a)*vec(b)+vec(b)*vec(c )+vec(c )*vec(a) .

Prove that vec(a)[(vec(b) + vec(c)) xx (vec(a) + 3vec(b) + 4vec(c))] = [ vec(a) vec(b) vec(c)]