Notation often helps makes the designation of objects simpler and can assist representing concepts by adding conciseness.
Here are some of the notation conventions we will use in discussing both graphs in Cartesian coordinate 3-spaces and mapping diagrams.

Cartesian 3 Space
Mapping Diagram
Numbers Planes
Lower case: $a,b,...$
Points on the $x,y$ or $z$  Axis
Lower case:$a,b,...$
Ordered triple of numbers
A Point
Triple of numbers: $(a,b,c)$

An Arrow
Pair of Numbers on 2 Axes: $a, b$
Arrow: $<a,b>$
Triple of Numbers on 3 Axes: $a,b,c$
Triangle: $<a,b,c>$
A Line/Plane
Pair of Numbers on 2 Axes: $a, b$
line: $[a,b]$
Triple of Numbers on 3 Axes: $a,b,c$
Plane: $[a,b,c]$

Point in 3 Space
Bold face/ Upper case: $\bf P = (p_1,p_2,p_3)$
Three Numbers on Axes: $p_1,p_2,p_3$
Arrows/Triangle: $<p_1,p_2,p_3>$
A Line
3 Numbers on Axes: $p_1,p_2, p_3$
A Plane: $[p_1,p_2, p_3]$
3 Arrows/Triangle in Mapping Diagram
 A Point
$ (v_1,v_2, v_3)$
Bold face/ Lower case:  $ \bf v$ $= <v_1,v_2,v_3>$
Numbers on Axes:  $v_1,v_2, v_3$;
Plane: $[v_1,v_2,v_3]$