Two vectors `vec(A)` and `vec( B)` are drawn from a common point and `vec(C)=vec(A)+vec(B)`

If two vectors vec(a) and vec (b) are such that |vec(a) . vec(b) | = |vec(a) xx vec(b)|, then find the angle the vectors vec(a) and vec (b)

If two vectors vec(a) and vec (b) are such that |vec(a) . vec(b) | = |vec(a) xx vec(b)|, then find the angle the vectors vec(a) and vec (b)

Two vectors vec(a) and vec (b) are such that |vec(a).vec(b)| = |vec(a) xx vec(b)| , then find the angle between the vectors vec(a) and vec(b) .

If any two of three vectors vec(a), vec(b), vec(c ) are parallel, then [vec(a)vec(b)vec(c )]= __________.

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) + vec(b) + vec(c) = vec(0) , then prove that vec(a) xx vec(b) = vec(b) xx vec(c) = vec(c) xx 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) 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