The question specifically asks to find or justify that a given vector is a normal vector to a plane, often as a standalone sub-question using cross products or dot product conditions.
Let P be the plane containing the vectors $(6,6,9)$ and $(7,8,10)$. Find a unit vector that is perpendicular to $(2,-3,4)$ and that lies in the plane P. (Note: all vectors are considered as line segments starting at the origin $(0,0,0)$. In particular the origin lies in the plane P.)