# Intersection between a plane and a line

• Asuralm

#### Asuralm

Hi all:
Given a plane ax+by+cz+d = 0, and a straight line, X = X0 + vt. What is an efficient way to compute the intersection point please? Also, is there any efficient method to determine if two points are located on the same side of the plane or on the different side of the plane?

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Thanks,

Tom

How to derive the answer should be obvious to you if you use a good enough notation!

Remember that for any t in R, there corresponds a point (x,y,z) on the line given by the equations:
$$x=x_{0}+v_{x,0}t, y=y_{0}+v_{y,0}t, z=z_{0}+v_{z,0}t$$

Furthermore, what requirement exists so that a point (x,y,z) is guaranteed to lie on the PLANE?

In particular, what equation for "t" do you get out of this?
(Remember that once you have found the required t-value, computing the specific values of the coordinates of the point is trivial)

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