If `vec(a),vec(b),vec(c)` are three non-coplanar unit vector such that `[vec(a),vec(b),vec(c)]=3` then [`vec(a) times vec(b), vec(b) times vec (c),vec(c) times vec(a)`] equals

If [vec(a) vec(b) vec(c)]=4 then [vec(a)times vec(b) vec(b)times vec(c)vec(c) times vec(a)] =

If vec(b) and vec(c) are two non-collinear vectors such that vec(a) || (vec(b) xx vec(c)) , then (vec(a) xx vec(b)).(vec(a) xx vec(c)) is equal to

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)+vec(b)+vec(c )=0 , then prove that : vec(a)xx vec(b)=vec(b)xx vec(c )=vec(c )xx vec(a) and hence, show that [vec(a)vec(b)vec(c )]=0 .

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

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)xx vec(b)=vec(c ), vec(b)xx vec(c )=vec(a) , prove that vec(a), vec(b), vec(c ) are mutually at right angles and |vec(b)|=1, |vec(c )|=|vec(a)| .

If vec(a), vec(b) and vec(c ) are mutually perpendicular unit vectors and vec(a)xx vec(b)=vec(c ) , show that vec(b)=vec(c )xx vec(a) and vec(a)=vec(b)xx vec(c ) .

If vec(A)+vec(B)+vec(C )=0 then vec(A)xx vec(B) is