Equation of line in 3d space passing in two points in a form of ax+by+cz+d=0

Question

I'm sorry for asking probably such easy question, but need help with this.. I need to get the parameters with the equation of a straight line passing through two points in 3d space.

ex:

line passes through
point1 (x1,y1,z1) point2 (x2,y2,z2)

I need the final equation in this parametric form

ax + by + cz + d = 0

I need to get a, b, c, and d parameters.

Answer 1

In 3d space your equation describes a plane, not a line.

The usual parametric form for a line would be $\vec{x} + t\vec{w}$, for $t$ a scalar, say.

In your case you can take $\vec{v} = (x_1,y_1,z_1)$ and $\vec{w} = (x_2,y_2,z_2) - (x_1,y_1,z_1)$ e.g.