Find four points on a plane

Question

This question comes from a coding project, so If there is any confusion please let me know.

I have two points (x1,y1,z1) (x2,y2,z2) which form a line. And I have a third point on the line (x3,y3,z3) where a plane across it and perpendicular to the line.

The (x3,y3,z3) calculate by [x1 + ratio * (x2 - x1), y1 + ratio * (y2 - y1), z1 + ratio * (z1 - z2)]; where ratio can be any number postive number below one.

Back on that plane, I need to figure out four points which layout like the graph below:

(I can't pasted a graph so I just describe it as much as I can)

Four points on the top right, top left, bottom right, botton left of the point(x3,y3,z3) and on that plane. Each takes 6 unit to the left or right and 6 unit to the up or down.

And suppose I know the line's rotation degree around the x-axis y-axis and z-axis which is given as pitch, roll, yall

How can I get the coordination of those four points?

Answer 1

step 1: find the slope, m, of the line P1 to P2

step 2: the first intercept is B_1 = P1 - P2*m

so the equation of the first line is y_ = m* x_ + B_1

step 3: find the NEGATIVE RECIPROCAL of the slope, M_|_ unless it is zero

step 4: the intercept of the perpendicular is B_2 = P3 - ( M_|_)* P2

step 5: calculates the intersection of these lines: (B_2 - B_1) / ( m - M_|_ )

step 6: calculates the points that are 6 units in all directions from the intersection

found in step 5