The gradient is a vector having (as coordinate components)
the partial derivatives of a function with respect to its variables.
Build from the given coordinate triples (2,-3,0) and (-3,-8,0)
the function y = [(-8 − -3)/(-3 − 2)]x + b which goes to
y = x + b. Then placement of (2,-3,0) in y = x + b gives
-3 = 2 + b or b (the y-intercept) equal to -5.
Then write F(x,y,z) is y = x − 5 or x − y = 5; z = 0 for
both coordinate triples and is here dropped from mention.
If the partial derivatives of x − y = 5 are defined for
(-3,-8), then the gradient of x − y = 5 is expressed
as ∇f (or "del-operator-f") equal to (∂f/∂x)i + (∂f/∂y)j
which here amounts to (1)i + (-1)j or i − j.
Drawing the vector i − j from the endpoint (-3,-8)
of the line segment between (-3,-8) and (2,-3)
will show a short vector directed to the right and
downward from (-3,-8) and perpendicular to
the line segment between (-3,-8) and (2,-3).
