Can we have physical quantities having magnitude and direction which are not vectors?

The physical quantities not having same dimensions are:

If A and B are two physical quantities having different dimensions then which of the following can denote a new physical quantity?

If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity ?

A physical quantity which has a direction and magnitude

The pairs of physical quantities that have the same dimensions is (are):

Of which physical quantity is the unit,.VA. ?

A vector has both magnitude and direaction . Does it mean that anything that has magnitude and direction is necessarily a vector ? The rotation of a body can be specified by the direction of the axis of rotation , and the angle of rotation about the axis . Does that make any rotation a vector ?

A physical quantity which has a direction:-

A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD= C 1n(BD) holds true. Then which of the combination is not a meaningful quantity :-

Which of the following physical quantities is an axial vector ?