How to locate a point in z axis given surface location x,y and z and the distance from the first point?

Question

I have location of a point P1 in x, y and z form. I want to find another point which is directly below this point (in z axis) at a distance d. This means that x & y co ordinates of P2 will be the same as that of P1. How to find the coordinates of P2 (z value)?

Answer 1

Maybe the most correct way would be to define a vector for the original point and one for the difference to the other point. Let a, b, c, represent the x, y, z coordinates for the known point and d is the distance of point 2 below point 1, then something like

v1 = {a, b, c}
diff = {0, 0, d}

and then subtract the two

v2 = v1 - diff

However, to merely get the coordinates of course all you really need to do is to define

v2 = {a, b, c-d}