To find the orientation of given 2 non collinear vectors in space

Question

If a and b are non collinear vectors,then how will the orientation of (a/mod(a))+(b/mod(b)) with respect to a and b vectors? Or will the vector be unit vector or something? Please explain. The answer could be any of these; a unit vector or in the plane of a and b or perpendicular to a and b or parallel to a and b.

Answer 1

It is generally not a unit vector, but it lies surely in the plane of a and b. Every vector of the form $\alpha a+\beta b$ lies there. It's actually the definition of the plane.