Question

if angle between a vector and b vector be 30 degree , then if i want to find the perpendicular unit vector , then the new vector will be perpendicular to both a and b . how is it possible. in figure, if if angle between a vector and b vector be 30 degree, then the angle between a and the new vector be 90 and b and the new vector be 60 . then how the new vector will be perpendicular to both a and b? please explain me with figure.