Vertical, perpendicular, plumb can mean situated at right angles to the plane of the horizon or extending from that plane at such an angle.
Vertical suggests a relation to the vertex or topmost point (see APEX 1 ); it is used most often when the thing so described actually extends upward from the plane of the horizon or from its base or support in such a direction that if its direction line were produced, it would reach the zenith.
Vertical is, of these terms, the most frequently applied to abstractions and the most common in extended use.
Perpendicular differs from vertical in being normally applied to things that extend upward or downward from the horizontal or both upward and downward; thus, one looks up or down the perpendicular face of a cliff.
Consequently, perpendicular is used more often than vertical to suggest little more than precipitousness or extreme steepness or stiffness and straightness of line.
Plumb is largely a builder’s term used particularly in judging the exact verticality or perpendicularity of something by its conformity to the direction of a plumb line.