Intersection of a Line and a Plane

Intersection of a Line and a Plane

For line:

$$x=x_1+a\lambda$$

$$y=y_1+b\lambda$$

$$z=z_1+c\lambda$$

and plane:

$$Ax+By+Cz+D=0$$

substitution gives:

$$A(x_1+a\lambda)+B(y_1+b\lambda)+C(z_1+c\lambda)+D=0$$

Hence:

$$\lambda=-\frac{Ax_1+By_1+Cz_1+D}{Aa+Bb+Cc}$$

provided:

$$Aa+Bb+Cc\neq0$$

Usage

- Used to find the point where a line intersects a plane.

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