All three points lie on a straight line. The equation for a line is: (x-x0)/L = (y-y0)/M = (z-z0)/N where (L,M,N) = the direction vector for that line. (x,y,z) = any point on the line. (x0,y0,z0) = a known point on the line.
So let's create the equation for a line passing through points a and b and see if point c lies on that line. (L,M,N) = a - b (L,M,N) = (2, 5, 3) - (3, 6, 2) = (2 - 3, 5 - 6, 3 - 2) = (-1, -1, 1) So we have (x-2)/-1 = (y-5)/-1 = (z - 3)/1 -(x-2) = -(y-5) = (z - 3)
Let's check the points. a(2,5,3) -(x-2) = -(y-5) = (z - 3) -(2-2) = -(5-5) = (3 - 3) 0 = 0 = 0 The above equation is true, so point a lies on the line.
b(3,6,2) -(x-2) = -(y-5) = (z - 3) -(3-2) = -(6-5) = (2 - 3) -1 = -1 = -1 The above equation is true, so point b lies on the line.
c(1,4,4) -(x-2) = -(y-5) = (z - 3) -(1-2) = -(4-5) = (4 - 3) 1 = 1 = 1 The above equation is true, so point c lies on the line.
All three points create true expressions for the formula, so all three points lie on a straight line.
