The standard parametrization for a line segment that runs from a point A to a point B is given by the function r(t) = A + t(B - A), where t is a variable that varies between 0 and 1.
In this case, the point A is (5, 0, 2) and point B is (0, 5, 0). Let's denote point A by its vector a = (5, 0, 2) and point B by its vector b = (0, 5, 0).
Therefore, to find the standard parametrization of the line segment from point A to point B, substitute points A and B into our standard parametrization function r(t) = A + t(B - A).
So, for the line segment between point A and point B, the parametrization function r(t) will be:
r(t) = (5, 0, 2) + t[(0, 5, 0) - (5, 0, 2)]
r(t) = (5, 0, 2) + t[-5, 5, -2]
r(t) = (5 - 5t, 0 + 5t, 2 - 2t)
This parametrization function describes every point between point A and point B depending on the value of the variable t.
When t = 0, we are at point A = (5, 0, 2).
As t increases, we move in a straight line from point A towards point B.
When t = 1, we have reached point B = (0, 5, 0).
So this parametrization function accurately describes the line segment from point A (5,0,2) to point B (0,5,0), with the motion along the line from point A to point B as t varies from
0 to 1. In a graph, the direction of increasing t would be from point A towards point B.